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Pinnacle Day: 19th Height and Distance
Height and Distance
In this chapter following concepts /
terminologies will be used.
Angle Of Elevation
The angle made by the line of sight with
the horizontal line is called the angle of
elevation.
Angle Of Depression
The angle made by the line of sight with
the horizontal line is called the angle of
depression.
Note: When we come near object, the
angle of elevation increases and when
we go away from the object, the angle of
elevation decreases.
Note: Angle of elevation and angle of
depression are always equal.
In this chapter trigonometric ratio and
concepts will be used which we have
discussed in detail in the trigonometry
chapter.
Some important relation
Case :- (1)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, 45° which is 30 m from the foot
of the tower. Find the height of the
tower?
Let the height of the tower be ‘H’
tan 45° =
??
30
1 = H = 30 m
??
30
?
Short Trick :- 1 30 m ?
1 ? ? = 30 m ? ?
Case :- (2)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, which is 30 m away from the
foot of the tower is 30°. Find the height
of the tower ?
Solution :-
Let , the height of the tower be ‘H’
tan 30° =
??
30
= H = m = 10 v3 m
1
v3
??
30
?
30
v3
Short Trick :-
v3 30 m ?
1 ? ? = m = 10 v3 m ? ?
30
v3
Case :- (3)
Example :- The angle of elevation of a
ladder leaning against a wall is 15° and
the foot of the ladder is 4 m away from
the wall. The length of the ladder is :
Solution :-
Let AB be the wall and AC be the ladder.
Then, ?ACB = 15° and BC = 4 m.
v3 + 1 4 m ?
2v2 ? ? = ? ?
8v2
v3 + 1
Case :- (4)
Example :- A man on the top of a vertical
observation tower observes a car
moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 45° . if
The height of the tower is 5 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = 1 And
total covered distance by the car
= BC = v3
So , ATQ
1 = 5 m
v3 = ? 5v3 ?
Case :- (5)
Example :- A man on the top of a
vertical observation tower observes a
car moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 60° .if
The height of the tower is 6 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = v3
And total covered distance by the car =
BD = 3
So , A/Q
v3 = 6 m
3 = ? 6v3 m ?
Variety Questions
Q.1. The shadow of a tower standing on
level ground is found to be 40 m longer
when the Sun's altitude is 30° than when
it was 45°. Find the height (in meters) of
the tower.
SSC CHSL Tier II 10/01/2024
(a) 10 (b) 20 ( 3 - 1 ) ( 3 - 1 )
(c) 20 (d) 10 ( 3 + 1 ) ( 3 + 1 )
Q.2. Two pillars of equal height stand on
either side of a roadway which is 150 m
wide. At a point in the road between
pillars, the elevations of the pillars are x°
and y° so that = = , ???????? °
2
5
, ???????? °
3
5
then the height of each pillar is :
SSC CGL Tier II ( 26/10/2023 )
www.ssccglpinnacle.com Download Pinnacle Exam Preparation App 106
Page 2
Pinnacle Day: 19th Height and Distance
Height and Distance
In this chapter following concepts /
terminologies will be used.
Angle Of Elevation
The angle made by the line of sight with
the horizontal line is called the angle of
elevation.
Angle Of Depression
The angle made by the line of sight with
the horizontal line is called the angle of
depression.
Note: When we come near object, the
angle of elevation increases and when
we go away from the object, the angle of
elevation decreases.
Note: Angle of elevation and angle of
depression are always equal.
In this chapter trigonometric ratio and
concepts will be used which we have
discussed in detail in the trigonometry
chapter.
Some important relation
Case :- (1)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, 45° which is 30 m from the foot
of the tower. Find the height of the
tower?
Let the height of the tower be ‘H’
tan 45° =
??
30
1 = H = 30 m
??
30
?
Short Trick :- 1 30 m ?
1 ? ? = 30 m ? ?
Case :- (2)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, which is 30 m away from the
foot of the tower is 30°. Find the height
of the tower ?
Solution :-
Let , the height of the tower be ‘H’
tan 30° =
??
30
= H = m = 10 v3 m
1
v3
??
30
?
30
v3
Short Trick :-
v3 30 m ?
1 ? ? = m = 10 v3 m ? ?
30
v3
Case :- (3)
Example :- The angle of elevation of a
ladder leaning against a wall is 15° and
the foot of the ladder is 4 m away from
the wall. The length of the ladder is :
Solution :-
Let AB be the wall and AC be the ladder.
Then, ?ACB = 15° and BC = 4 m.
v3 + 1 4 m ?
2v2 ? ? = ? ?
8v2
v3 + 1
Case :- (4)
Example :- A man on the top of a vertical
observation tower observes a car
moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 45° . if
The height of the tower is 5 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = 1 And
total covered distance by the car
= BC = v3
So , ATQ
1 = 5 m
v3 = ? 5v3 ?
Case :- (5)
Example :- A man on the top of a
vertical observation tower observes a
car moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 60° .if
The height of the tower is 6 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = v3
And total covered distance by the car =
BD = 3
So , A/Q
v3 = 6 m
3 = ? 6v3 m ?
Variety Questions
Q.1. The shadow of a tower standing on
level ground is found to be 40 m longer
when the Sun's altitude is 30° than when
it was 45°. Find the height (in meters) of
the tower.
SSC CHSL Tier II 10/01/2024
(a) 10 (b) 20 ( 3 - 1 ) ( 3 - 1 )
(c) 20 (d) 10 ( 3 + 1 ) ( 3 + 1 )
Q.2. Two pillars of equal height stand on
either side of a roadway which is 150 m
wide. At a point in the road between
pillars, the elevations of the pillars are x°
and y° so that = = , ???????? °
2
5
, ???????? °
3
5
then the height of each pillar is :
SSC CGL Tier II ( 26/10/2023 )
www.ssccglpinnacle.com Download Pinnacle Exam Preparation App 106
Pinnacle Day: 19th Height and Distance
(a) 39 m (b) 36 m (c) 42 m (d) 33 m
Q.3. Subhas, a 3.15 m tall tree, and an
11.25 m tall building are positioned such
that their feet on the ground are collinear
and the tree is located between Subhas
and the building. The tree is located at a
distance of 7.5 m from Subhas and at a
distance of 45 m from the building.
Further, the eyes of Subhas, the top of
the tree, and the top of the building fall in
one line. Find the height (in m) from the
ground at which Subhas' eyes are
situated.
SSC CHSL 09/08/2023 (4th Shift)
(a) 1.75 (b) 1.8 (c) 1.6 (d) 1.5
Q.4. From the top of an upright pole
17.75 m high, the angle of elevation of
the top of an upright tower was 60°. If the
tower was 57.75 m tall, how far away (in
m) from the foot of the pole was the foot
of the tower?
SSC CGL Tier II (03/03/2023)
(a) 40 (b) (c) (d) 3
151 3
6
77
4
3
40 3
3
Q.5. A pole 23 m long reaches a window
which is 3 m above the ground on one 5
side of a street. Keeping its foot at the
same point, the pole is turned to the
other side of the street to reach a
window 4 m high. What is the width 15
(in m) of the street?
SSC CGL 11/04/2021 (Afternoon)
(a) 17 (b) 35 (c) 39 (d) 22
Q.6. A person was standing on a road
near a mall. He was 1215 m away from
the mall and able to see the top of the
mall from the road in such a way that the
top of a tree, which is in between him and
the mall, was exactly in line of sight with
the top of the mall. The tree height is
20m and it is 60m away from him. How
tall (in m) is the mall?
SSC CPO 25/11/2020 (Morning)
(a) 405 (b) 250 (c) 300 (d) 375
Q.7. A pole stands vertically on a road,
which goes in the north- south direction.
P , Q are two points towards the north of
the pole, such that PQ = b, and the angles
of elevation of the top of the pole at P , Q
are , respectively. Then the height of a ß
the pole is:.
SSC CPO 09/12/2019 (Morning)
(a) (b)
??
?????? ß + ?????? a
??
?????? ß - ?????? a
(c) (d)
??
?????? ß - ?????? a
?? ?????? a
?????? ß
Q.8. A clock tower stands at the crossing
Of two roads which point in the
north-south and the east-west directions.
P ,Q,R and S are points on the roads due
north, east, south and west respectively,
where the angles of elevation of the top
of the tower are respectively,
. Then ( )
2
is equal to : a, ß, ? ?????? d
????
????
SSC CPO 09/12/2019 (Morning)
(a) (b)
??????
2
a + ??????
2
d
??????
2
? + ?? ????
2
ß
??????
2
a + ??????
2
ß
??????
2
? + ?? ????
2
d
(c) (d)
??????
2
a + ??????
2
ß
??????
2
? + ??????
2
d
??????
2
a + ??????
2
d
??????
2
? + ??????
2
ß
Q.9. From a point exactly midway
between the foot of two towers P and Q,
the angles of elevation of their tops are
and respectively. The ratio of the 30
?
60
?
height of P to that of Q is :
SSC CGL Tier II (12/09/2019)
(a) 1 : 3 (b) 1 : 2 (c) 1 : 2 (d) 2 : 3 3 3
Q.10. The angle of elevation of a ?ying
drone from a point on the ground is 60°.
After ?ying for 5 seconds the angle of
elevation drops to 30°. If the drone is
?ying horizontally at a constant height of
1000 m, the distance (in m) travelled 3
by the drone is:
SSC CPO 16/03/2019 (Afternoon)
(a) 2000 (b) 1000 (c) 3000 (d) 4000
Q.11. At a certain time of a day a tree 5.4
m height casts a shadow of 9 m. If a
pole casts a shadow of 13.5 m at the
same time, the height of the pole is:
SSC CPO 16/03/2019 (Morning)
(a) 8.1 m (b) 9.9 m (c) 7.2 m (d) 6.3 m
Q.12. What is the angle of elevation of
the sun from the top of a pillar, when its
height is equal to the length of its
shadow?
SSC CPO 15/03/2019 (Evening)
(a) 30° (b) 90° (c) 45° (d) 60°
Q.13. The top of a broken tree touches
the ground at a 60° angle, 45 meters
away from the root of the tree. What will
be the total height (in m) of the tree?
(Use = 1.73 and = 1.41) 3 2
SSC CPO 14/03/2019 (Evening)
(a) 153.45 (b) 141.3 (c) 167.85 (d) 137.24
Q.14. From the top of the 120 m high
lighthouse, the angle of depression of
two ships on opposite sides of the base
of the lighthouse is 30° and 60°. What is
the distance between the ships?
(rounded off)
SSC CPO 14 /03/2019 (Morning)
(a) 327 m (b) 127 m (c) 277 m (d) 177 m
Q.15. From the top of 75 m high tower,
the angle of depression of two points P
and Q on opposite side of the base of
the tower on level ground is and , such ? ?
that tan = and tan = . What is ?
3
4
?
5
8
the distance (in m) between the points P
and Q ?
SSC CPO 13/03/2019 (Morning)
(a) 190 (b) 200 (c) 180 (d) 220
Q.16. From the top of a 12 m high
building, the angle of elevation of the
top of the tower is 60° and the angle of
depression of the foot of the tower is , ?
such that tan = . What is the height ?
3
4
of the tower ? ( = 1.73) 3
SSC CPO 12/03/2019 (Evening)
(a) 41.41 (b) 36.22 (c) 39.68 (d) 37.95
Q.17. A ladder leaning against a wall
makes an angle with the horizontal a
ground such that tan = . If the foot a
3
4
of the ladder is 5 m away from the wall,
what is the length (in m) of the ladder?
SSC CPO 12/03/2019 (Morning)
(a) 5.25 (b) 3.75 (c) 6.25 (d) 4.5
Practice Questions
SSC CHSL 2023 Tier - 2
Q.18. A pole stands vertically on the
ground with the help of a 12-metre steel
wire tied to its top and a?xed on the
ground. If the steel wire makes an angle
of 30° with the horizontal ground, then
the height of the pole is equal to:
SSC CHSL Tier II 02/11/2023
(a) 8 meters (b) meters 6 3
(c) meters (d) 6 meters 8 3
Q.19. A man observed the top of an
electric pole at angles of elevation of 60°
and 30°, respectively, from two different
observation points P and Q . If the
distance between P and Q is 10 m, ?nd
the height of the pole (in m).
SSC CHSL Tier II 10/01/2024
(a) 5 (b) 5 (c) 15 (d) 15 3 3
SSC CGL 2023 Tier - 2
Q.20. From the top of a tower, the angle
of depression of the top of a 10 m high
building is 60°. If the distance between
the tower and the building is m, ?nd 50 3
the height of the tower.
SSC CGL Tier II ( 26/10/2023 )
(a) 150 m (b) 100 m (c) 160 m (d) 140 m
SSC CHSL 2023 Tier - 1
Q.21. A vertical pillar 42 cm long casts a
35 cm long shadow. At the same time, a
tower casts a shadow 25 m long. Find
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Page 3
Pinnacle Day: 19th Height and Distance
Height and Distance
In this chapter following concepts /
terminologies will be used.
Angle Of Elevation
The angle made by the line of sight with
the horizontal line is called the angle of
elevation.
Angle Of Depression
The angle made by the line of sight with
the horizontal line is called the angle of
depression.
Note: When we come near object, the
angle of elevation increases and when
we go away from the object, the angle of
elevation decreases.
Note: Angle of elevation and angle of
depression are always equal.
In this chapter trigonometric ratio and
concepts will be used which we have
discussed in detail in the trigonometry
chapter.
Some important relation
Case :- (1)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, 45° which is 30 m from the foot
of the tower. Find the height of the
tower?
Let the height of the tower be ‘H’
tan 45° =
??
30
1 = H = 30 m
??
30
?
Short Trick :- 1 30 m ?
1 ? ? = 30 m ? ?
Case :- (2)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, which is 30 m away from the
foot of the tower is 30°. Find the height
of the tower ?
Solution :-
Let , the height of the tower be ‘H’
tan 30° =
??
30
= H = m = 10 v3 m
1
v3
??
30
?
30
v3
Short Trick :-
v3 30 m ?
1 ? ? = m = 10 v3 m ? ?
30
v3
Case :- (3)
Example :- The angle of elevation of a
ladder leaning against a wall is 15° and
the foot of the ladder is 4 m away from
the wall. The length of the ladder is :
Solution :-
Let AB be the wall and AC be the ladder.
Then, ?ACB = 15° and BC = 4 m.
v3 + 1 4 m ?
2v2 ? ? = ? ?
8v2
v3 + 1
Case :- (4)
Example :- A man on the top of a vertical
observation tower observes a car
moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 45° . if
The height of the tower is 5 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = 1 And
total covered distance by the car
= BC = v3
So , ATQ
1 = 5 m
v3 = ? 5v3 ?
Case :- (5)
Example :- A man on the top of a
vertical observation tower observes a
car moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 60° .if
The height of the tower is 6 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = v3
And total covered distance by the car =
BD = 3
So , A/Q
v3 = 6 m
3 = ? 6v3 m ?
Variety Questions
Q.1. The shadow of a tower standing on
level ground is found to be 40 m longer
when the Sun's altitude is 30° than when
it was 45°. Find the height (in meters) of
the tower.
SSC CHSL Tier II 10/01/2024
(a) 10 (b) 20 ( 3 - 1 ) ( 3 - 1 )
(c) 20 (d) 10 ( 3 + 1 ) ( 3 + 1 )
Q.2. Two pillars of equal height stand on
either side of a roadway which is 150 m
wide. At a point in the road between
pillars, the elevations of the pillars are x°
and y° so that = = , ???????? °
2
5
, ???????? °
3
5
then the height of each pillar is :
SSC CGL Tier II ( 26/10/2023 )
www.ssccglpinnacle.com Download Pinnacle Exam Preparation App 106
Pinnacle Day: 19th Height and Distance
(a) 39 m (b) 36 m (c) 42 m (d) 33 m
Q.3. Subhas, a 3.15 m tall tree, and an
11.25 m tall building are positioned such
that their feet on the ground are collinear
and the tree is located between Subhas
and the building. The tree is located at a
distance of 7.5 m from Subhas and at a
distance of 45 m from the building.
Further, the eyes of Subhas, the top of
the tree, and the top of the building fall in
one line. Find the height (in m) from the
ground at which Subhas' eyes are
situated.
SSC CHSL 09/08/2023 (4th Shift)
(a) 1.75 (b) 1.8 (c) 1.6 (d) 1.5
Q.4. From the top of an upright pole
17.75 m high, the angle of elevation of
the top of an upright tower was 60°. If the
tower was 57.75 m tall, how far away (in
m) from the foot of the pole was the foot
of the tower?
SSC CGL Tier II (03/03/2023)
(a) 40 (b) (c) (d) 3
151 3
6
77
4
3
40 3
3
Q.5. A pole 23 m long reaches a window
which is 3 m above the ground on one 5
side of a street. Keeping its foot at the
same point, the pole is turned to the
other side of the street to reach a
window 4 m high. What is the width 15
(in m) of the street?
SSC CGL 11/04/2021 (Afternoon)
(a) 17 (b) 35 (c) 39 (d) 22
Q.6. A person was standing on a road
near a mall. He was 1215 m away from
the mall and able to see the top of the
mall from the road in such a way that the
top of a tree, which is in between him and
the mall, was exactly in line of sight with
the top of the mall. The tree height is
20m and it is 60m away from him. How
tall (in m) is the mall?
SSC CPO 25/11/2020 (Morning)
(a) 405 (b) 250 (c) 300 (d) 375
Q.7. A pole stands vertically on a road,
which goes in the north- south direction.
P , Q are two points towards the north of
the pole, such that PQ = b, and the angles
of elevation of the top of the pole at P , Q
are , respectively. Then the height of a ß
the pole is:.
SSC CPO 09/12/2019 (Morning)
(a) (b)
??
?????? ß + ?????? a
??
?????? ß - ?????? a
(c) (d)
??
?????? ß - ?????? a
?? ?????? a
?????? ß
Q.8. A clock tower stands at the crossing
Of two roads which point in the
north-south and the east-west directions.
P ,Q,R and S are points on the roads due
north, east, south and west respectively,
where the angles of elevation of the top
of the tower are respectively,
. Then ( )
2
is equal to : a, ß, ? ?????? d
????
????
SSC CPO 09/12/2019 (Morning)
(a) (b)
??????
2
a + ??????
2
d
??????
2
? + ?? ????
2
ß
??????
2
a + ??????
2
ß
??????
2
? + ?? ????
2
d
(c) (d)
??????
2
a + ??????
2
ß
??????
2
? + ??????
2
d
??????
2
a + ??????
2
d
??????
2
? + ??????
2
ß
Q.9. From a point exactly midway
between the foot of two towers P and Q,
the angles of elevation of their tops are
and respectively. The ratio of the 30
?
60
?
height of P to that of Q is :
SSC CGL Tier II (12/09/2019)
(a) 1 : 3 (b) 1 : 2 (c) 1 : 2 (d) 2 : 3 3 3
Q.10. The angle of elevation of a ?ying
drone from a point on the ground is 60°.
After ?ying for 5 seconds the angle of
elevation drops to 30°. If the drone is
?ying horizontally at a constant height of
1000 m, the distance (in m) travelled 3
by the drone is:
SSC CPO 16/03/2019 (Afternoon)
(a) 2000 (b) 1000 (c) 3000 (d) 4000
Q.11. At a certain time of a day a tree 5.4
m height casts a shadow of 9 m. If a
pole casts a shadow of 13.5 m at the
same time, the height of the pole is:
SSC CPO 16/03/2019 (Morning)
(a) 8.1 m (b) 9.9 m (c) 7.2 m (d) 6.3 m
Q.12. What is the angle of elevation of
the sun from the top of a pillar, when its
height is equal to the length of its
shadow?
SSC CPO 15/03/2019 (Evening)
(a) 30° (b) 90° (c) 45° (d) 60°
Q.13. The top of a broken tree touches
the ground at a 60° angle, 45 meters
away from the root of the tree. What will
be the total height (in m) of the tree?
(Use = 1.73 and = 1.41) 3 2
SSC CPO 14/03/2019 (Evening)
(a) 153.45 (b) 141.3 (c) 167.85 (d) 137.24
Q.14. From the top of the 120 m high
lighthouse, the angle of depression of
two ships on opposite sides of the base
of the lighthouse is 30° and 60°. What is
the distance between the ships?
(rounded off)
SSC CPO 14 /03/2019 (Morning)
(a) 327 m (b) 127 m (c) 277 m (d) 177 m
Q.15. From the top of 75 m high tower,
the angle of depression of two points P
and Q on opposite side of the base of
the tower on level ground is and , such ? ?
that tan = and tan = . What is ?
3
4
?
5
8
the distance (in m) between the points P
and Q ?
SSC CPO 13/03/2019 (Morning)
(a) 190 (b) 200 (c) 180 (d) 220
Q.16. From the top of a 12 m high
building, the angle of elevation of the
top of the tower is 60° and the angle of
depression of the foot of the tower is , ?
such that tan = . What is the height ?
3
4
of the tower ? ( = 1.73) 3
SSC CPO 12/03/2019 (Evening)
(a) 41.41 (b) 36.22 (c) 39.68 (d) 37.95
Q.17. A ladder leaning against a wall
makes an angle with the horizontal a
ground such that tan = . If the foot a
3
4
of the ladder is 5 m away from the wall,
what is the length (in m) of the ladder?
SSC CPO 12/03/2019 (Morning)
(a) 5.25 (b) 3.75 (c) 6.25 (d) 4.5
Practice Questions
SSC CHSL 2023 Tier - 2
Q.18. A pole stands vertically on the
ground with the help of a 12-metre steel
wire tied to its top and a?xed on the
ground. If the steel wire makes an angle
of 30° with the horizontal ground, then
the height of the pole is equal to:
SSC CHSL Tier II 02/11/2023
(a) 8 meters (b) meters 6 3
(c) meters (d) 6 meters 8 3
Q.19. A man observed the top of an
electric pole at angles of elevation of 60°
and 30°, respectively, from two different
observation points P and Q . If the
distance between P and Q is 10 m, ?nd
the height of the pole (in m).
SSC CHSL Tier II 10/01/2024
(a) 5 (b) 5 (c) 15 (d) 15 3 3
SSC CGL 2023 Tier - 2
Q.20. From the top of a tower, the angle
of depression of the top of a 10 m high
building is 60°. If the distance between
the tower and the building is m, ?nd 50 3
the height of the tower.
SSC CGL Tier II ( 26/10/2023 )
(a) 150 m (b) 100 m (c) 160 m (d) 140 m
SSC CHSL 2023 Tier - 1
Q.21. A vertical pillar 42 cm long casts a
35 cm long shadow. At the same time, a
tower casts a shadow 25 m long. Find
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Pinnacle Day: 19th Height and Distance
the height of the tower.
SSC CHSL 07/08/2023 (4th Shift)
(a) 28 m (b) 35 m (c) 32 m (d) 30 m
Q.22. Suhas, a 3.15 m tall tree, and a
building are positioned such that their
feet on the ground are collinear and the
tree is located between Suhas and the
building. The tree is located at a distance
of 7.5 m from Suhas and at a distance of
45 m from the building. Further, the eyes
of Suhas, the top of the tree, and the top
of the building fall in one line, and the
eyes of Suhas are at a height of 1.8 m
from the ground. Find the height (in m) of
the building.
SSC CHSL 14/08/2023 (2nd Shift)
(a) 11.25 (b) 11.50 (c) 10.25 (d) 10.75
Q.23. Suhas, a tree, and an 11.25 m tall
building are positioned such that their
feet on the ground are collinear and the
tree is located between Suhas and the
building. The tree is located at a distance
of 7.5 m from Suhas and at a distance of
45 m from the building. Further, the eyes
of Suhas, the top of the tree, and the top
of the building fall in one line, and the
eyes of Suhas are at a height of 1.8 m
from the ground. Find the height (in m) of
the tree.
SSC CHSL 17/08/2023 (2nd Shift)
(a) 3.00 (b) 3.30 (c) 3.15 (d) 3.45
SSC CGL 2023 Tier - 1
Q.24. A person standing at a distance
looks at a building having a height of
1000 metres. The angle between the top
of the building and the ground is 30°. At
what approximate distance (in metres) is
the person standing away from the
building.
SSC CGL 17/07/2023 (4th shift)
(a) 1000 (b) 936 (c) 1732 (d) 1542
Q.25. A vertical pole of 28m height casts
a 19.2m long shadow. At the same time,
?nd the length of the shadow cast by
another pole of 52.5m height.
SSC CGL 20/07/2023 (4th shift)
(a) 36 m (b) 35 m (c) 40 m (d) 30 m
SSC CGL 2022 Tier - 2
Q.26. Two ships are on the opposite side
of a lighthouse such that all three of
them are collinear. The angles of
depression of the two ships from the top
of the lighthouse are 30° and 60°. If the
ships are 230 m apart, then ?nd the 3
height of the light house (in m).
SSC CGL Tier II (02/03/2023)
(a) 175.4 (b) 165.2 (c) 172.5 (d) 180.5
Q.27. From the top of an upright pole 24
feet high, the angle of elevation of the 3
top of an upright tower was 60°. If the
foot of the pole was 60 feet away from
the foot of the tower, what tall (in feet)
was the tower?
SSC CGL Tier II (06/03/2023)
(a) 84 (b) 36 (c) 44 (d) 60 3 3 3 3
Q.28. The angle of elevation of the top of
a tower from the top of a building whose
height is 680 m is 45° and the angle of
elevation of the top of the same tower
from the foot of the same building is 60°.
What is the height (in m) of the tower?
SSC CGL Tier II (07/03/2023)
(a) 340(3 + v3) (b) 310(3 - v3)
(c) 310(3 + v3) (d) 340(3 - v3)
SSC CGL 2022 Tier - 1
Q.29. An airplane goes 14 km due east
and then 48 km due north. How far is it
from its initial position?
SSC CGL 13/12/2022 (3rd Shift)
(a) 14 km (b) 48 km (c) 50 km (d) 28 km
SSC CGL 2021 Tier - 2
Q.30. A person 1.8 metre tall is 30 3
metres away from a tower. If the angle of
elevation from his eye to the top of the
tower is 30 degree, then what is the
height ( in m) of the tower?
SSC CGL Tier II (08/08/2022)
(a) 32.5 (b) 37.8 (c) 30.5 (d) 31.8
SSC CHSL 2021 Tier - 1
Q.31. The foot of a ladder 25 m long is 7
m from the base of the building. If the
top of the ladder slips by 4 m, then by
how much distance will the foot of the
ladder slide?
SSC CHSL 24/05/2022 ( Morning )
(a) 9 m (b) 7 m (c) 6 m (d) 8 m
SSC CGL 2021 Tier - 1
Q.32. The angle of elevation of the top of
an un?nished tower at a point distant 78
m from its base is 30°. How much higher
must the tower be raised (in m) so that
the angle of elevation of the top of the
?nished tower at the same point will be
60°?
SSC CGL 11/04/2022(Morning)
(a) 78 (b) 80 (c) 52 (d) 26 3 3 3
Q.33. A vertical pole and a vertical tower
are on the same level ground in such a
way that, from the top of pole, the angle
of elevation of the top of the tower is 60°
and the angle of depression of the
bottom of the tower is 30°. If the height
of the pole is 24 m, then ?nd the height
of the tower (in m).
SSC CGL 12/04/2022(Morning)
(a) 24v3(v3 + 1) (b) 72
(c) 96 (d) 24(v3 + 1)
Q.34. The angle of elevation of the top of
a tall building from the points M and N at
the distances of 72m and 128m ,
respectively, from the base of the
building and in the same straight line
with it , are complementary . The height
of the building ( in m ) is ?
SSC CGL 12/04/2022(Afternoon)
(a) 84 (b) 96 (c) 80 (d) 90
Q.35. Exactly midway between the foot
of two towers P and Q, the angle of
elevation of their tops are 45° and 60°,
respectively. The ratio of the heights of P
and Q is:
SSC CGL 18/04/2022 (Morning)
(a) 1 : v3 (b) 3 : 1 (c) 1 : 3 (d) v3 : 1
Q.36. A poster is on top of a building. A
person is standing on the ground at a
distance of 50m from the building. The
angles of elevation to the top of the
poster and bottom of the poster are 45°
and 30° , respectively . What is 200% of
the height ( in m) of the poster?
SSC CGL 18/04/2022(afternoon)
(a) (3 - ) (b) (3 - )
25
3
3
75
3
3
(c) (3 - ) (d) (3 - )
50
3
3
100
3
3
SSC CGL 2020 Tier - 2
Q.37. Two pillars A and B of the same
height are on opposite sides of a road
which is 40 m wide. The angles of
elevation of the tops of the pillars A and
B are 30° and 45°, respectively, at a point
on the road between the pillars. What is
the distance( in m) of the point from the
foot of pillar A?
SSC CGL Tier II (03/02/2022)
(a) 40( - 1) (b) 20(2 - ) 3 3
(c) 20(3 - ) (d) 39 3 3
SSC CHSL 2020 Tier - 1
Q.38. As observed from the top of a
lighthouse, 42 m high above sea level,
The angle of depression of a ship sailing
directly towards it changes from 30° to
45°. The distance travelled by the ship
during the period of observation is:
SSC CHSL 04/08/2021 (Evening)
(a) 42(1 - ) (b) 42( + 1) 3 3
(c) 42( - 1) (d) 42 3
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Page 4
Pinnacle Day: 19th Height and Distance
Height and Distance
In this chapter following concepts /
terminologies will be used.
Angle Of Elevation
The angle made by the line of sight with
the horizontal line is called the angle of
elevation.
Angle Of Depression
The angle made by the line of sight with
the horizontal line is called the angle of
depression.
Note: When we come near object, the
angle of elevation increases and when
we go away from the object, the angle of
elevation decreases.
Note: Angle of elevation and angle of
depression are always equal.
In this chapter trigonometric ratio and
concepts will be used which we have
discussed in detail in the trigonometry
chapter.
Some important relation
Case :- (1)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, 45° which is 30 m from the foot
of the tower. Find the height of the
tower?
Let the height of the tower be ‘H’
tan 45° =
??
30
1 = H = 30 m
??
30
?
Short Trick :- 1 30 m ?
1 ? ? = 30 m ? ?
Case :- (2)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, which is 30 m away from the
foot of the tower is 30°. Find the height
of the tower ?
Solution :-
Let , the height of the tower be ‘H’
tan 30° =
??
30
= H = m = 10 v3 m
1
v3
??
30
?
30
v3
Short Trick :-
v3 30 m ?
1 ? ? = m = 10 v3 m ? ?
30
v3
Case :- (3)
Example :- The angle of elevation of a
ladder leaning against a wall is 15° and
the foot of the ladder is 4 m away from
the wall. The length of the ladder is :
Solution :-
Let AB be the wall and AC be the ladder.
Then, ?ACB = 15° and BC = 4 m.
v3 + 1 4 m ?
2v2 ? ? = ? ?
8v2
v3 + 1
Case :- (4)
Example :- A man on the top of a vertical
observation tower observes a car
moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 45° . if
The height of the tower is 5 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = 1 And
total covered distance by the car
= BC = v3
So , ATQ
1 = 5 m
v3 = ? 5v3 ?
Case :- (5)
Example :- A man on the top of a
vertical observation tower observes a
car moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 60° .if
The height of the tower is 6 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = v3
And total covered distance by the car =
BD = 3
So , A/Q
v3 = 6 m
3 = ? 6v3 m ?
Variety Questions
Q.1. The shadow of a tower standing on
level ground is found to be 40 m longer
when the Sun's altitude is 30° than when
it was 45°. Find the height (in meters) of
the tower.
SSC CHSL Tier II 10/01/2024
(a) 10 (b) 20 ( 3 - 1 ) ( 3 - 1 )
(c) 20 (d) 10 ( 3 + 1 ) ( 3 + 1 )
Q.2. Two pillars of equal height stand on
either side of a roadway which is 150 m
wide. At a point in the road between
pillars, the elevations of the pillars are x°
and y° so that = = , ???????? °
2
5
, ???????? °
3
5
then the height of each pillar is :
SSC CGL Tier II ( 26/10/2023 )
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Pinnacle Day: 19th Height and Distance
(a) 39 m (b) 36 m (c) 42 m (d) 33 m
Q.3. Subhas, a 3.15 m tall tree, and an
11.25 m tall building are positioned such
that their feet on the ground are collinear
and the tree is located between Subhas
and the building. The tree is located at a
distance of 7.5 m from Subhas and at a
distance of 45 m from the building.
Further, the eyes of Subhas, the top of
the tree, and the top of the building fall in
one line. Find the height (in m) from the
ground at which Subhas' eyes are
situated.
SSC CHSL 09/08/2023 (4th Shift)
(a) 1.75 (b) 1.8 (c) 1.6 (d) 1.5
Q.4. From the top of an upright pole
17.75 m high, the angle of elevation of
the top of an upright tower was 60°. If the
tower was 57.75 m tall, how far away (in
m) from the foot of the pole was the foot
of the tower?
SSC CGL Tier II (03/03/2023)
(a) 40 (b) (c) (d) 3
151 3
6
77
4
3
40 3
3
Q.5. A pole 23 m long reaches a window
which is 3 m above the ground on one 5
side of a street. Keeping its foot at the
same point, the pole is turned to the
other side of the street to reach a
window 4 m high. What is the width 15
(in m) of the street?
SSC CGL 11/04/2021 (Afternoon)
(a) 17 (b) 35 (c) 39 (d) 22
Q.6. A person was standing on a road
near a mall. He was 1215 m away from
the mall and able to see the top of the
mall from the road in such a way that the
top of a tree, which is in between him and
the mall, was exactly in line of sight with
the top of the mall. The tree height is
20m and it is 60m away from him. How
tall (in m) is the mall?
SSC CPO 25/11/2020 (Morning)
(a) 405 (b) 250 (c) 300 (d) 375
Q.7. A pole stands vertically on a road,
which goes in the north- south direction.
P , Q are two points towards the north of
the pole, such that PQ = b, and the angles
of elevation of the top of the pole at P , Q
are , respectively. Then the height of a ß
the pole is:.
SSC CPO 09/12/2019 (Morning)
(a) (b)
??
?????? ß + ?????? a
??
?????? ß - ?????? a
(c) (d)
??
?????? ß - ?????? a
?? ?????? a
?????? ß
Q.8. A clock tower stands at the crossing
Of two roads which point in the
north-south and the east-west directions.
P ,Q,R and S are points on the roads due
north, east, south and west respectively,
where the angles of elevation of the top
of the tower are respectively,
. Then ( )
2
is equal to : a, ß, ? ?????? d
????
????
SSC CPO 09/12/2019 (Morning)
(a) (b)
??????
2
a + ??????
2
d
??????
2
? + ?? ????
2
ß
??????
2
a + ??????
2
ß
??????
2
? + ?? ????
2
d
(c) (d)
??????
2
a + ??????
2
ß
??????
2
? + ??????
2
d
??????
2
a + ??????
2
d
??????
2
? + ??????
2
ß
Q.9. From a point exactly midway
between the foot of two towers P and Q,
the angles of elevation of their tops are
and respectively. The ratio of the 30
?
60
?
height of P to that of Q is :
SSC CGL Tier II (12/09/2019)
(a) 1 : 3 (b) 1 : 2 (c) 1 : 2 (d) 2 : 3 3 3
Q.10. The angle of elevation of a ?ying
drone from a point on the ground is 60°.
After ?ying for 5 seconds the angle of
elevation drops to 30°. If the drone is
?ying horizontally at a constant height of
1000 m, the distance (in m) travelled 3
by the drone is:
SSC CPO 16/03/2019 (Afternoon)
(a) 2000 (b) 1000 (c) 3000 (d) 4000
Q.11. At a certain time of a day a tree 5.4
m height casts a shadow of 9 m. If a
pole casts a shadow of 13.5 m at the
same time, the height of the pole is:
SSC CPO 16/03/2019 (Morning)
(a) 8.1 m (b) 9.9 m (c) 7.2 m (d) 6.3 m
Q.12. What is the angle of elevation of
the sun from the top of a pillar, when its
height is equal to the length of its
shadow?
SSC CPO 15/03/2019 (Evening)
(a) 30° (b) 90° (c) 45° (d) 60°
Q.13. The top of a broken tree touches
the ground at a 60° angle, 45 meters
away from the root of the tree. What will
be the total height (in m) of the tree?
(Use = 1.73 and = 1.41) 3 2
SSC CPO 14/03/2019 (Evening)
(a) 153.45 (b) 141.3 (c) 167.85 (d) 137.24
Q.14. From the top of the 120 m high
lighthouse, the angle of depression of
two ships on opposite sides of the base
of the lighthouse is 30° and 60°. What is
the distance between the ships?
(rounded off)
SSC CPO 14 /03/2019 (Morning)
(a) 327 m (b) 127 m (c) 277 m (d) 177 m
Q.15. From the top of 75 m high tower,
the angle of depression of two points P
and Q on opposite side of the base of
the tower on level ground is and , such ? ?
that tan = and tan = . What is ?
3
4
?
5
8
the distance (in m) between the points P
and Q ?
SSC CPO 13/03/2019 (Morning)
(a) 190 (b) 200 (c) 180 (d) 220
Q.16. From the top of a 12 m high
building, the angle of elevation of the
top of the tower is 60° and the angle of
depression of the foot of the tower is , ?
such that tan = . What is the height ?
3
4
of the tower ? ( = 1.73) 3
SSC CPO 12/03/2019 (Evening)
(a) 41.41 (b) 36.22 (c) 39.68 (d) 37.95
Q.17. A ladder leaning against a wall
makes an angle with the horizontal a
ground such that tan = . If the foot a
3
4
of the ladder is 5 m away from the wall,
what is the length (in m) of the ladder?
SSC CPO 12/03/2019 (Morning)
(a) 5.25 (b) 3.75 (c) 6.25 (d) 4.5
Practice Questions
SSC CHSL 2023 Tier - 2
Q.18. A pole stands vertically on the
ground with the help of a 12-metre steel
wire tied to its top and a?xed on the
ground. If the steel wire makes an angle
of 30° with the horizontal ground, then
the height of the pole is equal to:
SSC CHSL Tier II 02/11/2023
(a) 8 meters (b) meters 6 3
(c) meters (d) 6 meters 8 3
Q.19. A man observed the top of an
electric pole at angles of elevation of 60°
and 30°, respectively, from two different
observation points P and Q . If the
distance between P and Q is 10 m, ?nd
the height of the pole (in m).
SSC CHSL Tier II 10/01/2024
(a) 5 (b) 5 (c) 15 (d) 15 3 3
SSC CGL 2023 Tier - 2
Q.20. From the top of a tower, the angle
of depression of the top of a 10 m high
building is 60°. If the distance between
the tower and the building is m, ?nd 50 3
the height of the tower.
SSC CGL Tier II ( 26/10/2023 )
(a) 150 m (b) 100 m (c) 160 m (d) 140 m
SSC CHSL 2023 Tier - 1
Q.21. A vertical pillar 42 cm long casts a
35 cm long shadow. At the same time, a
tower casts a shadow 25 m long. Find
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Pinnacle Day: 19th Height and Distance
the height of the tower.
SSC CHSL 07/08/2023 (4th Shift)
(a) 28 m (b) 35 m (c) 32 m (d) 30 m
Q.22. Suhas, a 3.15 m tall tree, and a
building are positioned such that their
feet on the ground are collinear and the
tree is located between Suhas and the
building. The tree is located at a distance
of 7.5 m from Suhas and at a distance of
45 m from the building. Further, the eyes
of Suhas, the top of the tree, and the top
of the building fall in one line, and the
eyes of Suhas are at a height of 1.8 m
from the ground. Find the height (in m) of
the building.
SSC CHSL 14/08/2023 (2nd Shift)
(a) 11.25 (b) 11.50 (c) 10.25 (d) 10.75
Q.23. Suhas, a tree, and an 11.25 m tall
building are positioned such that their
feet on the ground are collinear and the
tree is located between Suhas and the
building. The tree is located at a distance
of 7.5 m from Suhas and at a distance of
45 m from the building. Further, the eyes
of Suhas, the top of the tree, and the top
of the building fall in one line, and the
eyes of Suhas are at a height of 1.8 m
from the ground. Find the height (in m) of
the tree.
SSC CHSL 17/08/2023 (2nd Shift)
(a) 3.00 (b) 3.30 (c) 3.15 (d) 3.45
SSC CGL 2023 Tier - 1
Q.24. A person standing at a distance
looks at a building having a height of
1000 metres. The angle between the top
of the building and the ground is 30°. At
what approximate distance (in metres) is
the person standing away from the
building.
SSC CGL 17/07/2023 (4th shift)
(a) 1000 (b) 936 (c) 1732 (d) 1542
Q.25. A vertical pole of 28m height casts
a 19.2m long shadow. At the same time,
?nd the length of the shadow cast by
another pole of 52.5m height.
SSC CGL 20/07/2023 (4th shift)
(a) 36 m (b) 35 m (c) 40 m (d) 30 m
SSC CGL 2022 Tier - 2
Q.26. Two ships are on the opposite side
of a lighthouse such that all three of
them are collinear. The angles of
depression of the two ships from the top
of the lighthouse are 30° and 60°. If the
ships are 230 m apart, then ?nd the 3
height of the light house (in m).
SSC CGL Tier II (02/03/2023)
(a) 175.4 (b) 165.2 (c) 172.5 (d) 180.5
Q.27. From the top of an upright pole 24
feet high, the angle of elevation of the 3
top of an upright tower was 60°. If the
foot of the pole was 60 feet away from
the foot of the tower, what tall (in feet)
was the tower?
SSC CGL Tier II (06/03/2023)
(a) 84 (b) 36 (c) 44 (d) 60 3 3 3 3
Q.28. The angle of elevation of the top of
a tower from the top of a building whose
height is 680 m is 45° and the angle of
elevation of the top of the same tower
from the foot of the same building is 60°.
What is the height (in m) of the tower?
SSC CGL Tier II (07/03/2023)
(a) 340(3 + v3) (b) 310(3 - v3)
(c) 310(3 + v3) (d) 340(3 - v3)
SSC CGL 2022 Tier - 1
Q.29. An airplane goes 14 km due east
and then 48 km due north. How far is it
from its initial position?
SSC CGL 13/12/2022 (3rd Shift)
(a) 14 km (b) 48 km (c) 50 km (d) 28 km
SSC CGL 2021 Tier - 2
Q.30. A person 1.8 metre tall is 30 3
metres away from a tower. If the angle of
elevation from his eye to the top of the
tower is 30 degree, then what is the
height ( in m) of the tower?
SSC CGL Tier II (08/08/2022)
(a) 32.5 (b) 37.8 (c) 30.5 (d) 31.8
SSC CHSL 2021 Tier - 1
Q.31. The foot of a ladder 25 m long is 7
m from the base of the building. If the
top of the ladder slips by 4 m, then by
how much distance will the foot of the
ladder slide?
SSC CHSL 24/05/2022 ( Morning )
(a) 9 m (b) 7 m (c) 6 m (d) 8 m
SSC CGL 2021 Tier - 1
Q.32. The angle of elevation of the top of
an un?nished tower at a point distant 78
m from its base is 30°. How much higher
must the tower be raised (in m) so that
the angle of elevation of the top of the
?nished tower at the same point will be
60°?
SSC CGL 11/04/2022(Morning)
(a) 78 (b) 80 (c) 52 (d) 26 3 3 3
Q.33. A vertical pole and a vertical tower
are on the same level ground in such a
way that, from the top of pole, the angle
of elevation of the top of the tower is 60°
and the angle of depression of the
bottom of the tower is 30°. If the height
of the pole is 24 m, then ?nd the height
of the tower (in m).
SSC CGL 12/04/2022(Morning)
(a) 24v3(v3 + 1) (b) 72
(c) 96 (d) 24(v3 + 1)
Q.34. The angle of elevation of the top of
a tall building from the points M and N at
the distances of 72m and 128m ,
respectively, from the base of the
building and in the same straight line
with it , are complementary . The height
of the building ( in m ) is ?
SSC CGL 12/04/2022(Afternoon)
(a) 84 (b) 96 (c) 80 (d) 90
Q.35. Exactly midway between the foot
of two towers P and Q, the angle of
elevation of their tops are 45° and 60°,
respectively. The ratio of the heights of P
and Q is:
SSC CGL 18/04/2022 (Morning)
(a) 1 : v3 (b) 3 : 1 (c) 1 : 3 (d) v3 : 1
Q.36. A poster is on top of a building. A
person is standing on the ground at a
distance of 50m from the building. The
angles of elevation to the top of the
poster and bottom of the poster are 45°
and 30° , respectively . What is 200% of
the height ( in m) of the poster?
SSC CGL 18/04/2022(afternoon)
(a) (3 - ) (b) (3 - )
25
3
3
75
3
3
(c) (3 - ) (d) (3 - )
50
3
3
100
3
3
SSC CGL 2020 Tier - 2
Q.37. Two pillars A and B of the same
height are on opposite sides of a road
which is 40 m wide. The angles of
elevation of the tops of the pillars A and
B are 30° and 45°, respectively, at a point
on the road between the pillars. What is
the distance( in m) of the point from the
foot of pillar A?
SSC CGL Tier II (03/02/2022)
(a) 40( - 1) (b) 20(2 - ) 3 3
(c) 20(3 - ) (d) 39 3 3
SSC CHSL 2020 Tier - 1
Q.38. As observed from the top of a
lighthouse, 42 m high above sea level,
The angle of depression of a ship sailing
directly towards it changes from 30° to
45°. The distance travelled by the ship
during the period of observation is:
SSC CHSL 04/08/2021 (Evening)
(a) 42(1 - ) (b) 42( + 1) 3 3
(c) 42( - 1) (d) 42 3
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Pinnacle Day: 19th Height and Distance
SSC CPO 2020 Tier - 1
Q.39. A ladder leaning against a wall
makes an with the horizontal ground ?
such that cos = . If the height of the ?
5
13
top of the ladder from the wall is 18m,
then what is the distance (in cm) of the
foot of the ladder from the wall?
SSC CPO 23/11/2020 (Morning)
(a) 19.5 (b) 13 (c) 7.5 (d) 18
Q.40. A person was standing on a road
near a mall. He was 1425 m away from
the mall and able to see the top of the
mall from the road in such a way that the
top of the tree, which is in between him
and the mall, was exactly in line of sight
with the top of the mall. The tree height
is 10m and it is 30m away from him.
How tall (in m) is the mall?
SSC CPO 23/11/2020 (Morning)
(a) 475 (b) 300 (c) 425 (d) 525
Q.41. The length of the shadow of a
vertical pole on the ground is 18m. If the
angle of elevation of the sun at that time
is such that cos = , then what is ?, ?
12
13
the height (in m) of the pole ?
SSC CPO 23/11/2020 (Evening)
(a) 18 (b) 9 (c) 7.5 (d) 12
SSC CGL 2019 Tier - 2
Q.42. From the top of a hill 240m high
the angle of depression of the top and of
the bottom of a pole are 30° and 60°,
respectively. The difference (in m)
between the height of the pole and its
distance from the hill is :
SSC CGL Tier II (16/11/2020)
(a) (b) 80 ( 2 - 3 ) 120 ( 3 - 1 )
(c) (d) 120 ( 2 - 3 ) 80 ( 3 - 1 )
Q.43. The length of the shadow of the
vertical tower on level ground increases
by 10m when the altitude of the sun
changes from 45° to 30°. The height of
the tower is:
SSC CGL Tier II (18/11/2020)
(a) 10( ) m (b) 10 m 3 + 1 3
(c) 5 m (d) 5( + 1) m 3 3
SSC CPO 2019 Tier - 1
Q.44. A kite is ?ying at a height of 123 m.
The thread attached to it is assumed to
be stretched straight and makes an angle
of 60° with the level ground. The length
of the string is(nearest to a whole
number)
SSC CPO 11/12/2019 (Morning)
(a) 140 m (b) 139 m (c) 142 m (d) 138 m
Q.45. From the top of a lamp post of
height x metres, two objects on the
ground on the same side of it ( and in line
with the foot of the lamp post) are
observed at the angle of depression of
30 degree and 60 degree respectively.
The distance between the objects is
32 m. The value of x is : 3
SSC CPO 12/12/2019 (Morning)
(a) 54 (b) 48 (c) 45 (d) 36
Q.46. The angle of elevation of the top of
a tree from a point on the ground which
is 300 m away from the tree is 30°. When
the tree grew up, its angle of elevation of
the top of it became 60° from the same
point. How much did the tree (in m)
grow? (nearest to an integer)
SSC CPO 12/12/2019 (Evening)
(a) 342 (b) 364 (c) 384 (d) 346
Q.47. A pole of length 7 m is ?xed
vertically on the top of a tower. The angle
of elevation of the top of the pole
observed from a point on the ground is
60° and the angle of depression of the
same point on the ground from the top of
the tower is 45°. The height (in m) of the
tower is:
SSC CPO 13/12/2019 (Morning)
(a) 7(2 (b) 3 - 1 )
7
2
( 3 + 2 )
(c) 7 (d) 3
7
2
( 3 + 1 )
Q.48. The angles of elevation of a pole
from two points which are 75 m and 48
m away from its base are and a ß
respectively. If and are a ß
complementary, then the height of the
tower is :
SSC CPO 13/12/2019 (Evening)
(a) 54.5 m (b) 60 m (c) 61.5 m (d) 50 m
SSC CGL 2018 Tier - 2
Q.49. From the top of a tower, the angles
of depression of two objects on the
ground on the same side of it, are
observed to be 60° and 30° respectively
and the distance between the objects is
400 m. The height (in m) of the tower 3
is :
SSC CGL Tier II (11/09/2019)
(a) 800 (b) 800 (c) 600 (d) 600 3 3
SSC CPO 2018 Tier - 1
Q.50. A ladder leaning against a wall
makes an angle with the horizontal ?
ground such that sin = . If the foot ?
12
13
of the ladder is 7.5 m from a wall, then
what is the height of the point from
where the top of the ladder touches the
wall?
SSC CPO 12/03/2019(Evening)
(a) 15 m (b) 8 m (c) 18 m (d) 12 m
Q.51. A ladder attached to the wall
makes an angle of 60° to the horizontal
of the land. If the lower end of the ladder
is 10 meters away from the wall, what
will be the length of the ladder?
SSC CPO 14/03/2019 (Evening)
(a) 20 m (b) 40 m (c) 17.3 m (d) 34.6 m
Q.52. A boy is standing near a pole
which is 2.7 m high and the angle of
elevation is 30° The distance (in m) of
the boy from the pole is ( = 1.73) 3
SSC CPO 16/03/2019 (Morning)
(a) 4.42 (b) 4.53 (c) 4.68 (d) 4.63
Answer Key :-
1.(c) 2.(b) 3.(b) 4.(d)
5.(c) 6.(a) 7.(b) 8.(c)
9.(a) 10.(a) 11.(a) 12.(c)
13.(c) 14.(c) 15.(d) 16.(c)
17.(c) 18.(d) 19.(a) 20.(c)
21.(d) 22.(a) 23.(c) 24.(c)
25.(a) 26.(c) 27.(a) 28.(a)
29.(c) 30.(d) 31.(d) 32.(c)
33.(c) 34.(b) 35.(a) 36.(d)
37.(c) 38.(c) 39.(c) 40.(a)
41.(c) 42.(a) 43.(d) 44.(c)
45.(b) 46.(d) 47.(d) 48.(b)
49.(c) 50.(c) 51.(a) 52.(c)
Solutions :-
Sol.1.(c)
?????? 30° =
h
h + 40
1
3
=
h
h + 40
h + 40 = 3 h
? height of tower ( h ) =
40
3 - 1
= meter 20 ( 3 + 1 )
Sol.2.(b) Let AB and CD be the two pillars
of equal height
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Page 5
Pinnacle Day: 19th Height and Distance
Height and Distance
In this chapter following concepts /
terminologies will be used.
Angle Of Elevation
The angle made by the line of sight with
the horizontal line is called the angle of
elevation.
Angle Of Depression
The angle made by the line of sight with
the horizontal line is called the angle of
depression.
Note: When we come near object, the
angle of elevation increases and when
we go away from the object, the angle of
elevation decreases.
Note: Angle of elevation and angle of
depression are always equal.
In this chapter trigonometric ratio and
concepts will be used which we have
discussed in detail in the trigonometry
chapter.
Some important relation
Case :- (1)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, 45° which is 30 m from the foot
of the tower. Find the height of the
tower?
Let the height of the tower be ‘H’
tan 45° =
??
30
1 = H = 30 m
??
30
?
Short Trick :- 1 30 m ?
1 ? ? = 30 m ? ?
Case :- (2)
Example :- The angle of elevation of the
top of a tower from a point on the
ground, which is 30 m away from the
foot of the tower is 30°. Find the height
of the tower ?
Solution :-
Let , the height of the tower be ‘H’
tan 30° =
??
30
= H = m = 10 v3 m
1
v3
??
30
?
30
v3
Short Trick :-
v3 30 m ?
1 ? ? = m = 10 v3 m ? ?
30
v3
Case :- (3)
Example :- The angle of elevation of a
ladder leaning against a wall is 15° and
the foot of the ladder is 4 m away from
the wall. The length of the ladder is :
Solution :-
Let AB be the wall and AC be the ladder.
Then, ?ACB = 15° and BC = 4 m.
v3 + 1 4 m ?
2v2 ? ? = ? ?
8v2
v3 + 1
Case :- (4)
Example :- A man on the top of a vertical
observation tower observes a car
moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 45° . if
The height of the tower is 5 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = 1 And
total covered distance by the car
= BC = v3
So , ATQ
1 = 5 m
v3 = ? 5v3 ?
Case :- (5)
Example :- A man on the top of a
vertical observation tower observes a
car moving at a uniform speed coming
directly towards it and the angle of
depression to change from 30° to 60° .if
The height of the tower is 6 m then ?nd
the value of the total covered distance by
the car ?
Solution :-
Let AB = Height of tower = v3
And total covered distance by the car =
BD = 3
So , A/Q
v3 = 6 m
3 = ? 6v3 m ?
Variety Questions
Q.1. The shadow of a tower standing on
level ground is found to be 40 m longer
when the Sun's altitude is 30° than when
it was 45°. Find the height (in meters) of
the tower.
SSC CHSL Tier II 10/01/2024
(a) 10 (b) 20 ( 3 - 1 ) ( 3 - 1 )
(c) 20 (d) 10 ( 3 + 1 ) ( 3 + 1 )
Q.2. Two pillars of equal height stand on
either side of a roadway which is 150 m
wide. At a point in the road between
pillars, the elevations of the pillars are x°
and y° so that = = , ???????? °
2
5
, ???????? °
3
5
then the height of each pillar is :
SSC CGL Tier II ( 26/10/2023 )
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Pinnacle Day: 19th Height and Distance
(a) 39 m (b) 36 m (c) 42 m (d) 33 m
Q.3. Subhas, a 3.15 m tall tree, and an
11.25 m tall building are positioned such
that their feet on the ground are collinear
and the tree is located between Subhas
and the building. The tree is located at a
distance of 7.5 m from Subhas and at a
distance of 45 m from the building.
Further, the eyes of Subhas, the top of
the tree, and the top of the building fall in
one line. Find the height (in m) from the
ground at which Subhas' eyes are
situated.
SSC CHSL 09/08/2023 (4th Shift)
(a) 1.75 (b) 1.8 (c) 1.6 (d) 1.5
Q.4. From the top of an upright pole
17.75 m high, the angle of elevation of
the top of an upright tower was 60°. If the
tower was 57.75 m tall, how far away (in
m) from the foot of the pole was the foot
of the tower?
SSC CGL Tier II (03/03/2023)
(a) 40 (b) (c) (d) 3
151 3
6
77
4
3
40 3
3
Q.5. A pole 23 m long reaches a window
which is 3 m above the ground on one 5
side of a street. Keeping its foot at the
same point, the pole is turned to the
other side of the street to reach a
window 4 m high. What is the width 15
(in m) of the street?
SSC CGL 11/04/2021 (Afternoon)
(a) 17 (b) 35 (c) 39 (d) 22
Q.6. A person was standing on a road
near a mall. He was 1215 m away from
the mall and able to see the top of the
mall from the road in such a way that the
top of a tree, which is in between him and
the mall, was exactly in line of sight with
the top of the mall. The tree height is
20m and it is 60m away from him. How
tall (in m) is the mall?
SSC CPO 25/11/2020 (Morning)
(a) 405 (b) 250 (c) 300 (d) 375
Q.7. A pole stands vertically on a road,
which goes in the north- south direction.
P , Q are two points towards the north of
the pole, such that PQ = b, and the angles
of elevation of the top of the pole at P , Q
are , respectively. Then the height of a ß
the pole is:.
SSC CPO 09/12/2019 (Morning)
(a) (b)
??
?????? ß + ?????? a
??
?????? ß - ?????? a
(c) (d)
??
?????? ß - ?????? a
?? ?????? a
?????? ß
Q.8. A clock tower stands at the crossing
Of two roads which point in the
north-south and the east-west directions.
P ,Q,R and S are points on the roads due
north, east, south and west respectively,
where the angles of elevation of the top
of the tower are respectively,
. Then ( )
2
is equal to : a, ß, ? ?????? d
????
????
SSC CPO 09/12/2019 (Morning)
(a) (b)
??????
2
a + ??????
2
d
??????
2
? + ?? ????
2
ß
??????
2
a + ??????
2
ß
??????
2
? + ?? ????
2
d
(c) (d)
??????
2
a + ??????
2
ß
??????
2
? + ??????
2
d
??????
2
a + ??????
2
d
??????
2
? + ??????
2
ß
Q.9. From a point exactly midway
between the foot of two towers P and Q,
the angles of elevation of their tops are
and respectively. The ratio of the 30
?
60
?
height of P to that of Q is :
SSC CGL Tier II (12/09/2019)
(a) 1 : 3 (b) 1 : 2 (c) 1 : 2 (d) 2 : 3 3 3
Q.10. The angle of elevation of a ?ying
drone from a point on the ground is 60°.
After ?ying for 5 seconds the angle of
elevation drops to 30°. If the drone is
?ying horizontally at a constant height of
1000 m, the distance (in m) travelled 3
by the drone is:
SSC CPO 16/03/2019 (Afternoon)
(a) 2000 (b) 1000 (c) 3000 (d) 4000
Q.11. At a certain time of a day a tree 5.4
m height casts a shadow of 9 m. If a
pole casts a shadow of 13.5 m at the
same time, the height of the pole is:
SSC CPO 16/03/2019 (Morning)
(a) 8.1 m (b) 9.9 m (c) 7.2 m (d) 6.3 m
Q.12. What is the angle of elevation of
the sun from the top of a pillar, when its
height is equal to the length of its
shadow?
SSC CPO 15/03/2019 (Evening)
(a) 30° (b) 90° (c) 45° (d) 60°
Q.13. The top of a broken tree touches
the ground at a 60° angle, 45 meters
away from the root of the tree. What will
be the total height (in m) of the tree?
(Use = 1.73 and = 1.41) 3 2
SSC CPO 14/03/2019 (Evening)
(a) 153.45 (b) 141.3 (c) 167.85 (d) 137.24
Q.14. From the top of the 120 m high
lighthouse, the angle of depression of
two ships on opposite sides of the base
of the lighthouse is 30° and 60°. What is
the distance between the ships?
(rounded off)
SSC CPO 14 /03/2019 (Morning)
(a) 327 m (b) 127 m (c) 277 m (d) 177 m
Q.15. From the top of 75 m high tower,
the angle of depression of two points P
and Q on opposite side of the base of
the tower on level ground is and , such ? ?
that tan = and tan = . What is ?
3
4
?
5
8
the distance (in m) between the points P
and Q ?
SSC CPO 13/03/2019 (Morning)
(a) 190 (b) 200 (c) 180 (d) 220
Q.16. From the top of a 12 m high
building, the angle of elevation of the
top of the tower is 60° and the angle of
depression of the foot of the tower is , ?
such that tan = . What is the height ?
3
4
of the tower ? ( = 1.73) 3
SSC CPO 12/03/2019 (Evening)
(a) 41.41 (b) 36.22 (c) 39.68 (d) 37.95
Q.17. A ladder leaning against a wall
makes an angle with the horizontal a
ground such that tan = . If the foot a
3
4
of the ladder is 5 m away from the wall,
what is the length (in m) of the ladder?
SSC CPO 12/03/2019 (Morning)
(a) 5.25 (b) 3.75 (c) 6.25 (d) 4.5
Practice Questions
SSC CHSL 2023 Tier - 2
Q.18. A pole stands vertically on the
ground with the help of a 12-metre steel
wire tied to its top and a?xed on the
ground. If the steel wire makes an angle
of 30° with the horizontal ground, then
the height of the pole is equal to:
SSC CHSL Tier II 02/11/2023
(a) 8 meters (b) meters 6 3
(c) meters (d) 6 meters 8 3
Q.19. A man observed the top of an
electric pole at angles of elevation of 60°
and 30°, respectively, from two different
observation points P and Q . If the
distance between P and Q is 10 m, ?nd
the height of the pole (in m).
SSC CHSL Tier II 10/01/2024
(a) 5 (b) 5 (c) 15 (d) 15 3 3
SSC CGL 2023 Tier - 2
Q.20. From the top of a tower, the angle
of depression of the top of a 10 m high
building is 60°. If the distance between
the tower and the building is m, ?nd 50 3
the height of the tower.
SSC CGL Tier II ( 26/10/2023 )
(a) 150 m (b) 100 m (c) 160 m (d) 140 m
SSC CHSL 2023 Tier - 1
Q.21. A vertical pillar 42 cm long casts a
35 cm long shadow. At the same time, a
tower casts a shadow 25 m long. Find
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Pinnacle Day: 19th Height and Distance
the height of the tower.
SSC CHSL 07/08/2023 (4th Shift)
(a) 28 m (b) 35 m (c) 32 m (d) 30 m
Q.22. Suhas, a 3.15 m tall tree, and a
building are positioned such that their
feet on the ground are collinear and the
tree is located between Suhas and the
building. The tree is located at a distance
of 7.5 m from Suhas and at a distance of
45 m from the building. Further, the eyes
of Suhas, the top of the tree, and the top
of the building fall in one line, and the
eyes of Suhas are at a height of 1.8 m
from the ground. Find the height (in m) of
the building.
SSC CHSL 14/08/2023 (2nd Shift)
(a) 11.25 (b) 11.50 (c) 10.25 (d) 10.75
Q.23. Suhas, a tree, and an 11.25 m tall
building are positioned such that their
feet on the ground are collinear and the
tree is located between Suhas and the
building. The tree is located at a distance
of 7.5 m from Suhas and at a distance of
45 m from the building. Further, the eyes
of Suhas, the top of the tree, and the top
of the building fall in one line, and the
eyes of Suhas are at a height of 1.8 m
from the ground. Find the height (in m) of
the tree.
SSC CHSL 17/08/2023 (2nd Shift)
(a) 3.00 (b) 3.30 (c) 3.15 (d) 3.45
SSC CGL 2023 Tier - 1
Q.24. A person standing at a distance
looks at a building having a height of
1000 metres. The angle between the top
of the building and the ground is 30°. At
what approximate distance (in metres) is
the person standing away from the
building.
SSC CGL 17/07/2023 (4th shift)
(a) 1000 (b) 936 (c) 1732 (d) 1542
Q.25. A vertical pole of 28m height casts
a 19.2m long shadow. At the same time,
?nd the length of the shadow cast by
another pole of 52.5m height.
SSC CGL 20/07/2023 (4th shift)
(a) 36 m (b) 35 m (c) 40 m (d) 30 m
SSC CGL 2022 Tier - 2
Q.26. Two ships are on the opposite side
of a lighthouse such that all three of
them are collinear. The angles of
depression of the two ships from the top
of the lighthouse are 30° and 60°. If the
ships are 230 m apart, then ?nd the 3
height of the light house (in m).
SSC CGL Tier II (02/03/2023)
(a) 175.4 (b) 165.2 (c) 172.5 (d) 180.5
Q.27. From the top of an upright pole 24
feet high, the angle of elevation of the 3
top of an upright tower was 60°. If the
foot of the pole was 60 feet away from
the foot of the tower, what tall (in feet)
was the tower?
SSC CGL Tier II (06/03/2023)
(a) 84 (b) 36 (c) 44 (d) 60 3 3 3 3
Q.28. The angle of elevation of the top of
a tower from the top of a building whose
height is 680 m is 45° and the angle of
elevation of the top of the same tower
from the foot of the same building is 60°.
What is the height (in m) of the tower?
SSC CGL Tier II (07/03/2023)
(a) 340(3 + v3) (b) 310(3 - v3)
(c) 310(3 + v3) (d) 340(3 - v3)
SSC CGL 2022 Tier - 1
Q.29. An airplane goes 14 km due east
and then 48 km due north. How far is it
from its initial position?
SSC CGL 13/12/2022 (3rd Shift)
(a) 14 km (b) 48 km (c) 50 km (d) 28 km
SSC CGL 2021 Tier - 2
Q.30. A person 1.8 metre tall is 30 3
metres away from a tower. If the angle of
elevation from his eye to the top of the
tower is 30 degree, then what is the
height ( in m) of the tower?
SSC CGL Tier II (08/08/2022)
(a) 32.5 (b) 37.8 (c) 30.5 (d) 31.8
SSC CHSL 2021 Tier - 1
Q.31. The foot of a ladder 25 m long is 7
m from the base of the building. If the
top of the ladder slips by 4 m, then by
how much distance will the foot of the
ladder slide?
SSC CHSL 24/05/2022 ( Morning )
(a) 9 m (b) 7 m (c) 6 m (d) 8 m
SSC CGL 2021 Tier - 1
Q.32. The angle of elevation of the top of
an un?nished tower at a point distant 78
m from its base is 30°. How much higher
must the tower be raised (in m) so that
the angle of elevation of the top of the
?nished tower at the same point will be
60°?
SSC CGL 11/04/2022(Morning)
(a) 78 (b) 80 (c) 52 (d) 26 3 3 3
Q.33. A vertical pole and a vertical tower
are on the same level ground in such a
way that, from the top of pole, the angle
of elevation of the top of the tower is 60°
and the angle of depression of the
bottom of the tower is 30°. If the height
of the pole is 24 m, then ?nd the height
of the tower (in m).
SSC CGL 12/04/2022(Morning)
(a) 24v3(v3 + 1) (b) 72
(c) 96 (d) 24(v3 + 1)
Q.34. The angle of elevation of the top of
a tall building from the points M and N at
the distances of 72m and 128m ,
respectively, from the base of the
building and in the same straight line
with it , are complementary . The height
of the building ( in m ) is ?
SSC CGL 12/04/2022(Afternoon)
(a) 84 (b) 96 (c) 80 (d) 90
Q.35. Exactly midway between the foot
of two towers P and Q, the angle of
elevation of their tops are 45° and 60°,
respectively. The ratio of the heights of P
and Q is:
SSC CGL 18/04/2022 (Morning)
(a) 1 : v3 (b) 3 : 1 (c) 1 : 3 (d) v3 : 1
Q.36. A poster is on top of a building. A
person is standing on the ground at a
distance of 50m from the building. The
angles of elevation to the top of the
poster and bottom of the poster are 45°
and 30° , respectively . What is 200% of
the height ( in m) of the poster?
SSC CGL 18/04/2022(afternoon)
(a) (3 - ) (b) (3 - )
25
3
3
75
3
3
(c) (3 - ) (d) (3 - )
50
3
3
100
3
3
SSC CGL 2020 Tier - 2
Q.37. Two pillars A and B of the same
height are on opposite sides of a road
which is 40 m wide. The angles of
elevation of the tops of the pillars A and
B are 30° and 45°, respectively, at a point
on the road between the pillars. What is
the distance( in m) of the point from the
foot of pillar A?
SSC CGL Tier II (03/02/2022)
(a) 40( - 1) (b) 20(2 - ) 3 3
(c) 20(3 - ) (d) 39 3 3
SSC CHSL 2020 Tier - 1
Q.38. As observed from the top of a
lighthouse, 42 m high above sea level,
The angle of depression of a ship sailing
directly towards it changes from 30° to
45°. The distance travelled by the ship
during the period of observation is:
SSC CHSL 04/08/2021 (Evening)
(a) 42(1 - ) (b) 42( + 1) 3 3
(c) 42( - 1) (d) 42 3
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Pinnacle Day: 19th Height and Distance
SSC CPO 2020 Tier - 1
Q.39. A ladder leaning against a wall
makes an with the horizontal ground ?
such that cos = . If the height of the ?
5
13
top of the ladder from the wall is 18m,
then what is the distance (in cm) of the
foot of the ladder from the wall?
SSC CPO 23/11/2020 (Morning)
(a) 19.5 (b) 13 (c) 7.5 (d) 18
Q.40. A person was standing on a road
near a mall. He was 1425 m away from
the mall and able to see the top of the
mall from the road in such a way that the
top of the tree, which is in between him
and the mall, was exactly in line of sight
with the top of the mall. The tree height
is 10m and it is 30m away from him.
How tall (in m) is the mall?
SSC CPO 23/11/2020 (Morning)
(a) 475 (b) 300 (c) 425 (d) 525
Q.41. The length of the shadow of a
vertical pole on the ground is 18m. If the
angle of elevation of the sun at that time
is such that cos = , then what is ?, ?
12
13
the height (in m) of the pole ?
SSC CPO 23/11/2020 (Evening)
(a) 18 (b) 9 (c) 7.5 (d) 12
SSC CGL 2019 Tier - 2
Q.42. From the top of a hill 240m high
the angle of depression of the top and of
the bottom of a pole are 30° and 60°,
respectively. The difference (in m)
between the height of the pole and its
distance from the hill is :
SSC CGL Tier II (16/11/2020)
(a) (b) 80 ( 2 - 3 ) 120 ( 3 - 1 )
(c) (d) 120 ( 2 - 3 ) 80 ( 3 - 1 )
Q.43. The length of the shadow of the
vertical tower on level ground increases
by 10m when the altitude of the sun
changes from 45° to 30°. The height of
the tower is:
SSC CGL Tier II (18/11/2020)
(a) 10( ) m (b) 10 m 3 + 1 3
(c) 5 m (d) 5( + 1) m 3 3
SSC CPO 2019 Tier - 1
Q.44. A kite is ?ying at a height of 123 m.
The thread attached to it is assumed to
be stretched straight and makes an angle
of 60° with the level ground. The length
of the string is(nearest to a whole
number)
SSC CPO 11/12/2019 (Morning)
(a) 140 m (b) 139 m (c) 142 m (d) 138 m
Q.45. From the top of a lamp post of
height x metres, two objects on the
ground on the same side of it ( and in line
with the foot of the lamp post) are
observed at the angle of depression of
30 degree and 60 degree respectively.
The distance between the objects is
32 m. The value of x is : 3
SSC CPO 12/12/2019 (Morning)
(a) 54 (b) 48 (c) 45 (d) 36
Q.46. The angle of elevation of the top of
a tree from a point on the ground which
is 300 m away from the tree is 30°. When
the tree grew up, its angle of elevation of
the top of it became 60° from the same
point. How much did the tree (in m)
grow? (nearest to an integer)
SSC CPO 12/12/2019 (Evening)
(a) 342 (b) 364 (c) 384 (d) 346
Q.47. A pole of length 7 m is ?xed
vertically on the top of a tower. The angle
of elevation of the top of the pole
observed from a point on the ground is
60° and the angle of depression of the
same point on the ground from the top of
the tower is 45°. The height (in m) of the
tower is:
SSC CPO 13/12/2019 (Morning)
(a) 7(2 (b) 3 - 1 )
7
2
( 3 + 2 )
(c) 7 (d) 3
7
2
( 3 + 1 )
Q.48. The angles of elevation of a pole
from two points which are 75 m and 48
m away from its base are and a ß
respectively. If and are a ß
complementary, then the height of the
tower is :
SSC CPO 13/12/2019 (Evening)
(a) 54.5 m (b) 60 m (c) 61.5 m (d) 50 m
SSC CGL 2018 Tier - 2
Q.49. From the top of a tower, the angles
of depression of two objects on the
ground on the same side of it, are
observed to be 60° and 30° respectively
and the distance between the objects is
400 m. The height (in m) of the tower 3
is :
SSC CGL Tier II (11/09/2019)
(a) 800 (b) 800 (c) 600 (d) 600 3 3
SSC CPO 2018 Tier - 1
Q.50. A ladder leaning against a wall
makes an angle with the horizontal ?
ground such that sin = . If the foot ?
12
13
of the ladder is 7.5 m from a wall, then
what is the height of the point from
where the top of the ladder touches the
wall?
SSC CPO 12/03/2019(Evening)
(a) 15 m (b) 8 m (c) 18 m (d) 12 m
Q.51. A ladder attached to the wall
makes an angle of 60° to the horizontal
of the land. If the lower end of the ladder
is 10 meters away from the wall, what
will be the length of the ladder?
SSC CPO 14/03/2019 (Evening)
(a) 20 m (b) 40 m (c) 17.3 m (d) 34.6 m
Q.52. A boy is standing near a pole
which is 2.7 m high and the angle of
elevation is 30° The distance (in m) of
the boy from the pole is ( = 1.73) 3
SSC CPO 16/03/2019 (Morning)
(a) 4.42 (b) 4.53 (c) 4.68 (d) 4.63
Answer Key :-
1.(c) 2.(b) 3.(b) 4.(d)
5.(c) 6.(a) 7.(b) 8.(c)
9.(a) 10.(a) 11.(a) 12.(c)
13.(c) 14.(c) 15.(d) 16.(c)
17.(c) 18.(d) 19.(a) 20.(c)
21.(d) 22.(a) 23.(c) 24.(c)
25.(a) 26.(c) 27.(a) 28.(a)
29.(c) 30.(d) 31.(d) 32.(c)
33.(c) 34.(b) 35.(a) 36.(d)
37.(c) 38.(c) 39.(c) 40.(a)
41.(c) 42.(a) 43.(d) 44.(c)
45.(b) 46.(d) 47.(d) 48.(b)
49.(c) 50.(c) 51.(a) 52.(c)
Solutions :-
Sol.1.(c)
?????? 30° =
h
h + 40
1
3
=
h
h + 40
h + 40 = 3 h
? height of tower ( h ) =
40
3 - 1
= meter 20 ( 3 + 1 )
Sol.2.(b) Let AB and CD be the two pillars
of equal height
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Pinnacle Day: 19th Height and Distance
= = or ???????? °
????
????
2
5
6
15
= = or ???????? °
????
????
3
5
6
10
ATQ,
15 + 10 = 25 unit ---------------- 150 m
Then, 6 unit ---------------- × 6 = 36 m
150
25
Sol.3.(b)
EC = SP = 7.5 + 45 = 52.5 metre
BP = 11.25 metre - ??
? ? ?????? ? ??????
= = =
????
????
????
????
?
7 . 5
52 . 5
????
????
?
????
????
1
7
6 units = = 8.1 metre 11 . 25 - 3 . 15 ( )
TO (1 unit) = = 1.35 metre
8 . 1
6
SE = OD = = 1.8 meter 3 . 15 - 1 . 35 ( )
Sol.4.(d)
Angle 30° : 60° : 90° ?
Side 1 : : 2 ? 3
In ABC , ?
units = 40m ? 1 unit = m 3
40 3
3
So, The foot of the tower is m
40 3
3
away from the foot of the pole.
Sol.5.(c)
Let P be the ?xed point of the pole and B
and D are two windows.,
In ABP , AP = ? ( 23 )
2
- ( 3 5 )
2
= = = 22 m. 529 - 45 484
In DPC, PC = ? ( 23 )
2
- ( 4 15 )
2
= = = 17 m. 529 - 240 289
So, width of street = 22 + 17= 39 m
Sol.6.(a)
we have to ?nd out the length of AB
ABC MDC(by AAA rule) ? ~ ?
= x = = 405 m
??
20
1215
60
?
1215 × 20
60
Sol.7.(b) Let the pole length be AB
In ABP , we have ; ?
tan = BP = AB cot a
????
????
? a
In ABQ, we have ; ?
tan = BQ = AB cot ß
????
????
? ß
Now, b = BQ - BP
b = AB cot - AB cot = AB(cot -cot ) ß a ß a
AB =
??
?????? ß - ?????? a
Sol.8.(c)
Let OA be a straight tower.
P , Q, R and S are points on the roads due
north, east, south and west respectively.
In ? POQ and ?ORS
PQ
2
= PO
2
+ OQ
2
RS
2
= OR
2
+ OS
2
= ---------- (1)
( ???? )
2
( ???? )
2
?? ??
2
+ ?? ??
2
?? ??
2
+ ?? ??
2
Here, ?AOQ = ?AOP = ?AOR = ?AOS
= 90°(as AO is a straight tower)
Now,
the angle of elevation are a, ß, and d. ?
In ?AOP , , tana = OP = AO cota
????
????
?
In ?AOS, tand = OS = OA cotd
????
????
?
Similarly, OQ = AO cotß and OR = AO ?????? ?
Putting the value of PO, OQ, OR, OS in
eqn (1), we have
=
( ???? )
2
( ???? )
2
( ?????????? a )
2
+ ( ?????????? ß)
2
( ?????????? ?)
2
+ ( ?????????? d)
2
=
???? ??
2
a+ ???? ??
2
ß
???? ??
2
?+ ???? ??
2
d
Sol.9.(a)
Let the height of tower P and Q be AD
and BE respectively and C be the
midpoint of DE.
From the given ?gure, we have ;
Required ratio = AD : BE = 1 : 3
Sol.10.(a)
In ACB, we have : ?
tan 60° = =
1000 3
????
? 3
1000 3
????
BC = 1000 m
In EDB, we have : ?
tan30° = =
1000 3
????
?
1
3
1000 3
????
BD = 3000 m
Distance covered by drone = BD – BC
= 3000 – 1000 = 2000 m
Sol.11.(a) Let the height of the pole be h.
ATQ , =
h
13 . 5
5 . 4
9
9h = 72.9 h = 8.1 m ?
Sol.12.(c)
Let AB and BC be the length of pole and
and the length of shadow respectively
AB = BC (given)
tan = = 1 = tan 45° = 45° ?
????
????
? ?
Short trick : If the height of an object and
length of its shadow is equal. Then, the
angle is 45°
Sol.13.(c)
Let BD be the total height of the tree.
AD = AC (given)
Here, 1 unit = 45 m
Then, unit = m 3 45 3
and 2 unit ?= 45 × 2 = 90 m
So, the total height of tree = + 90 45 3
= 77.85 + 90 = 167.85 m
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FAQs on SSC CGL Previous Year Questions (2023 - 18): Height and Distance - SSC CGL Mathematics Previous Year Paper (Topic-wise)
| 1. What is the basic concept of height and distance in mathematics? |  |
Ans. Height and distance involve determining the height or distance of an object or angle based on given information such as angles of elevation or depression.
| 2. How can we calculate the height of a building using the concept of height and distance? | |
Ans. To calculate the height of a building, we can use the angle of elevation from a known distance away from the building and trigonometric ratios such as tangent.
| 3. What is the angle of depression in height and distance problems? | |
Ans. The angle of depression is the angle below the horizontal line when viewing an object from a higher point. It is used to calculate the distance between the observer and the object.
| 4. How can we find the distance between two objects using height and distance concepts? | |
Ans. To find the distance between two objects, we can use the angles of elevation or depression from each object to a common point and apply trigonometric ratios such as tangent.
| 5. Can height and distance problems be solved without using trigonometry? | |
Ans. Yes, height and distance problems can also be solved using basic geometry concepts and properties of similar triangles, although trigonometry often provides a quicker and more accurate solution.
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