RD Sharma Class 11 Solutions Chapter - Measurement of Angles | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


4. Measurement of Angles
Exercise 4.1
1. Question
Find the degree measure corresponding to the following radian measures (Use p = )
(i)  (ii) - (iii) 
c
 (iv) (-3)
c
 (v) 11
c
 (vi) 1
c
Answer
We know that p rad = 180° ? 1 rad = 180°/ p
(i) Given 
= (36 × 9) °
= 324°
(ii) Given 
= (30 × -5) °
= -(150) °
(iii) Given 
= (36 × 18) °
= 648°
(iv) Given (-3) 
c
Page 2


4. Measurement of Angles
Exercise 4.1
1. Question
Find the degree measure corresponding to the following radian measures (Use p = )
(i)  (ii) - (iii) 
c
 (iv) (-3)
c
 (v) 11
c
 (vi) 1
c
Answer
We know that p rad = 180° ? 1 rad = 180°/ p
(i) Given 
= (36 × 9) °
= 324°
(ii) Given 
= (30 × -5) °
= -(150) °
(iii) Given 
= (36 × 18) °
= 648°
(iv) Given (-3) 
c
= -(171° 49’ 5.45”)
˜ -(171° 49’ 5”)
(v) Given 11
c
= (90 × 7) °
= 630°
(vi) Given 1
c
= (57° 16’ 21.81”)
˜ (57° 16’ 22”)
2. Question
Find the radian measure corresponding to the following degree measures:
(i) 300
0
 (ii) 35
0
 (iii) -56
0
 (iv)135
0
 (v) -300
0
(vi) 7
0
 30’ (vii) 125
0
 30’ (viii) -47
o
 30’
Answer
We know that 180° = p rad ? 1° = p/ 180 rad
(i) Given 300°
(ii) Given 35°
Page 3


4. Measurement of Angles
Exercise 4.1
1. Question
Find the degree measure corresponding to the following radian measures (Use p = )
(i)  (ii) - (iii) 
c
 (iv) (-3)
c
 (v) 11
c
 (vi) 1
c
Answer
We know that p rad = 180° ? 1 rad = 180°/ p
(i) Given 
= (36 × 9) °
= 324°
(ii) Given 
= (30 × -5) °
= -(150) °
(iii) Given 
= (36 × 18) °
= 648°
(iv) Given (-3) 
c
= -(171° 49’ 5.45”)
˜ -(171° 49’ 5”)
(v) Given 11
c
= (90 × 7) °
= 630°
(vi) Given 1
c
= (57° 16’ 21.81”)
˜ (57° 16’ 22”)
2. Question
Find the radian measure corresponding to the following degree measures:
(i) 300
0
 (ii) 35
0
 (iii) -56
0
 (iv)135
0
 (v) -300
0
(vi) 7
0
 30’ (vii) 125
0
 30’ (viii) -47
o
 30’
Answer
We know that 180° = p rad ? 1° = p/ 180 rad
(i) Given 300°
(ii) Given 35°
(iii) Given -56°
(iv) Given 135°
(v) Given -300°
(vi) Given 7° 30’
We know that 30’ = (1/2)°
? 7° 30’ = (7 1/2) °
(vii) Given 125° 30’
We know that 30’ = (1/2)°
? 125° 30’ = (1251/2) °
(viii) Given -47° 30’
We know that 30’ = (1/2)°
? -47° 30’ = -(471/2) °
Page 4


4. Measurement of Angles
Exercise 4.1
1. Question
Find the degree measure corresponding to the following radian measures (Use p = )
(i)  (ii) - (iii) 
c
 (iv) (-3)
c
 (v) 11
c
 (vi) 1
c
Answer
We know that p rad = 180° ? 1 rad = 180°/ p
(i) Given 
= (36 × 9) °
= 324°
(ii) Given 
= (30 × -5) °
= -(150) °
(iii) Given 
= (36 × 18) °
= 648°
(iv) Given (-3) 
c
= -(171° 49’ 5.45”)
˜ -(171° 49’ 5”)
(v) Given 11
c
= (90 × 7) °
= 630°
(vi) Given 1
c
= (57° 16’ 21.81”)
˜ (57° 16’ 22”)
2. Question
Find the radian measure corresponding to the following degree measures:
(i) 300
0
 (ii) 35
0
 (iii) -56
0
 (iv)135
0
 (v) -300
0
(vi) 7
0
 30’ (vii) 125
0
 30’ (viii) -47
o
 30’
Answer
We know that 180° = p rad ? 1° = p/ 180 rad
(i) Given 300°
(ii) Given 35°
(iii) Given -56°
(iv) Given 135°
(v) Given -300°
(vi) Given 7° 30’
We know that 30’ = (1/2)°
? 7° 30’ = (7 1/2) °
(vii) Given 125° 30’
We know that 30’ = (1/2)°
? 125° 30’ = (1251/2) °
(viii) Given -47° 30’
We know that 30’ = (1/2)°
? -47° 30’ = -(471/2) °
3. Question
The difference between the two acute angles of a right-angled triangle is 2p/5 radians. Express the angles in
degrees.
Answer
Given the difference between the two acute angles of a right-angled triangle is 2p/5 radians.
We know that p rad = 180° ? 1 rad = 180°/ p
Given 
= (36 × 2) °
= 72°
Let one acute angle be x° and the other acute angle be 90° - x°.
Then,
? x° - (90° - x°) = 72°
? 2x° - 90° = 72°
? 2x° = 72° + 90°
? 2x° = 162°
? x° = 162°/ 2
? x° = 81° and 90° - x° = 90° - 81° = 9°
4. Question
One angle of a triangle is  grades, and another is  degrees while the third is radians. Express all
the angles in degrees.
Answer
Given one angle of a triangle is 2x/3 grades and another is 3x/2 degree while the third is px/75 radians.
We know that 
We know that p rad = 180° ? 1 rad = 180°/ p
Given 
We know that the sum of the angles of a triangle is 180°.
Page 5


4. Measurement of Angles
Exercise 4.1
1. Question
Find the degree measure corresponding to the following radian measures (Use p = )
(i)  (ii) - (iii) 
c
 (iv) (-3)
c
 (v) 11
c
 (vi) 1
c
Answer
We know that p rad = 180° ? 1 rad = 180°/ p
(i) Given 
= (36 × 9) °
= 324°
(ii) Given 
= (30 × -5) °
= -(150) °
(iii) Given 
= (36 × 18) °
= 648°
(iv) Given (-3) 
c
= -(171° 49’ 5.45”)
˜ -(171° 49’ 5”)
(v) Given 11
c
= (90 × 7) °
= 630°
(vi) Given 1
c
= (57° 16’ 21.81”)
˜ (57° 16’ 22”)
2. Question
Find the radian measure corresponding to the following degree measures:
(i) 300
0
 (ii) 35
0
 (iii) -56
0
 (iv)135
0
 (v) -300
0
(vi) 7
0
 30’ (vii) 125
0
 30’ (viii) -47
o
 30’
Answer
We know that 180° = p rad ? 1° = p/ 180 rad
(i) Given 300°
(ii) Given 35°
(iii) Given -56°
(iv) Given 135°
(v) Given -300°
(vi) Given 7° 30’
We know that 30’ = (1/2)°
? 7° 30’ = (7 1/2) °
(vii) Given 125° 30’
We know that 30’ = (1/2)°
? 125° 30’ = (1251/2) °
(viii) Given -47° 30’
We know that 30’ = (1/2)°
? -47° 30’ = -(471/2) °
3. Question
The difference between the two acute angles of a right-angled triangle is 2p/5 radians. Express the angles in
degrees.
Answer
Given the difference between the two acute angles of a right-angled triangle is 2p/5 radians.
We know that p rad = 180° ? 1 rad = 180°/ p
Given 
= (36 × 2) °
= 72°
Let one acute angle be x° and the other acute angle be 90° - x°.
Then,
? x° - (90° - x°) = 72°
? 2x° - 90° = 72°
? 2x° = 72° + 90°
? 2x° = 162°
? x° = 162°/ 2
? x° = 81° and 90° - x° = 90° - 81° = 9°
4. Question
One angle of a triangle is  grades, and another is  degrees while the third is radians. Express all
the angles in degrees.
Answer
Given one angle of a triangle is 2x/3 grades and another is 3x/2 degree while the third is px/75 radians.
We know that 
We know that p rad = 180° ? 1 rad = 180°/ p
Given 
We know that the sum of the angles of a triangle is 180°.
? 45 x° = 180° × 10°
? 45 x° = 1800°
? x° = 1800°/ 45°
? x = 40°
? The angles of the triangle are
5. Question
Find the magnitude, in radians and degrees, of the interior angle of a regular:
(i) Pentagon (ii) Octagon (iii) Heptagon (iv) Duodecagon.
Answer
We know that the sum of the interior angles of a polygon = (n – 2) p
And each angle of polygon 
(i) Pentagon
Number of sides in pentagon = 5
Sum of interior angles of pentagon = (5 – 2) p = 3p
? Each angle of pentagon 
(ii) Octagon
Number of sides in octagon = 8
Sum of interior angles of octagon = (8 – 2) p = 6p
? Each angle of octagon 
(iii) Heptagon
Number of sides in heptagon = 7
Sum of interior angles of heptagon = (7 – 2) p = 5p
? Each angle of heptagon 
(iv) Duodecagon
Number of sides in duodecagon = 12
Sum of interior angles of duodecagon = (12 – 2) p = 10p
? Each angle of duodecagon