Selina Textbook Solutions: Height and Distance | Mathematics Class 10 ICSE PDF Download

 Page 1


Heights and Distances 
 
Exercise 22 A 
Question 1. 
The height of a tree is v3 times the length of its shadow. Find the angle of elevation of 
the sun. 
 
Solution: 
 
Question 2. 
The angle of elevation of the top of a tower from a point on the ground and at a distance 
of 160 m from its foot, is found to be 60
o
. Find the height of the tower. 
 
Solution: 
 
 
Page 2


Heights and Distances 
 
Exercise 22 A 
Question 1. 
The height of a tree is v3 times the length of its shadow. Find the angle of elevation of 
the sun. 
 
Solution: 
 
Question 2. 
The angle of elevation of the top of a tower from a point on the ground and at a distance 
of 160 m from its foot, is found to be 60
o
. Find the height of the tower. 
 
Solution: 
 
 
 
Question 3. 
A ladder is placed along a wall such that its upper end is resting against a vertical wall. 
The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 
68
o
 with the ground. Find the height, upto which the ladder reaches. 
 
Solution: 
 
 
Question 4. 
Two persons are standing on the opposite sides of a tower. They observe the angles of 
elevation of the top of the tower to be 30
o
 and 38
o
 respectively. Find the distance 
between them, if the height of the tower is 50 m. 
Page 3


Heights and Distances 
 
Exercise 22 A 
Question 1. 
The height of a tree is v3 times the length of its shadow. Find the angle of elevation of 
the sun. 
 
Solution: 
 
Question 2. 
The angle of elevation of the top of a tower from a point on the ground and at a distance 
of 160 m from its foot, is found to be 60
o
. Find the height of the tower. 
 
Solution: 
 
 
 
Question 3. 
A ladder is placed along a wall such that its upper end is resting against a vertical wall. 
The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 
68
o
 with the ground. Find the height, upto which the ladder reaches. 
 
Solution: 
 
 
Question 4. 
Two persons are standing on the opposite sides of a tower. They observe the angles of 
elevation of the top of the tower to be 30
o
 and 38
o
 respectively. Find the distance 
between them, if the height of the tower is 50 m. 
Solution: 
 
Question 5. 
A kite is attached to a string. Find the length of the string, when the height of the kite is 
60 m and the string makes an angle 30
o
 with the ground. 
 
Solution: 
 
 
Page 4


Heights and Distances 
 
Exercise 22 A 
Question 1. 
The height of a tree is v3 times the length of its shadow. Find the angle of elevation of 
the sun. 
 
Solution: 
 
Question 2. 
The angle of elevation of the top of a tower from a point on the ground and at a distance 
of 160 m from its foot, is found to be 60
o
. Find the height of the tower. 
 
Solution: 
 
 
 
Question 3. 
A ladder is placed along a wall such that its upper end is resting against a vertical wall. 
The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 
68
o
 with the ground. Find the height, upto which the ladder reaches. 
 
Solution: 
 
 
Question 4. 
Two persons are standing on the opposite sides of a tower. They observe the angles of 
elevation of the top of the tower to be 30
o
 and 38
o
 respectively. Find the distance 
between them, if the height of the tower is 50 m. 
Solution: 
 
Question 5. 
A kite is attached to a string. Find the length of the string, when the height of the kite is 
60 m and the string makes an angle 30
o
 with the ground. 
 
Solution: 
 
 
 
Question 6. 
A boy, 1.6 m tall, is 20 m away from a tower and observes the angle of elevation of the 
top of the tower to be (i) 45
o
, (ii) 60
o
. Find the height of the tower in each case. 
 
Solution: 
 
 
Question 7. 
The upper part of a tree, broken over by the wind, makes an angle of 45
o
 with the ground 
and the distance from the root to the point where the top of the tree touches the ground 
is 15 m. What was the height of the tree before it was broken? 
Page 5


Heights and Distances 
 
Exercise 22 A 
Question 1. 
The height of a tree is v3 times the length of its shadow. Find the angle of elevation of 
the sun. 
 
Solution: 
 
Question 2. 
The angle of elevation of the top of a tower from a point on the ground and at a distance 
of 160 m from its foot, is found to be 60
o
. Find the height of the tower. 
 
Solution: 
 
 
 
Question 3. 
A ladder is placed along a wall such that its upper end is resting against a vertical wall. 
The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of 
68
o
 with the ground. Find the height, upto which the ladder reaches. 
 
Solution: 
 
 
Question 4. 
Two persons are standing on the opposite sides of a tower. They observe the angles of 
elevation of the top of the tower to be 30
o
 and 38
o
 respectively. Find the distance 
between them, if the height of the tower is 50 m. 
Solution: 
 
Question 5. 
A kite is attached to a string. Find the length of the string, when the height of the kite is 
60 m and the string makes an angle 30
o
 with the ground. 
 
Solution: 
 
 
 
Question 6. 
A boy, 1.6 m tall, is 20 m away from a tower and observes the angle of elevation of the 
top of the tower to be (i) 45
o
, (ii) 60
o
. Find the height of the tower in each case. 
 
Solution: 
 
 
Question 7. 
The upper part of a tree, broken over by the wind, makes an angle of 45
o
 with the ground 
and the distance from the root to the point where the top of the tree touches the ground 
is 15 m. What was the height of the tree before it was broken? 
Solution: 
 
Question 8. 
The angle of elevation of the top of an unfinished tower at a point distance 80 m from 
its base is 30
o
. How much higher must the tower be raised so that its angle of elevation 
at the same point may be 60
o
? 
 
Solution: