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RD Sharma solutions for Class 11 Mathematics chapter 4 - Measurement of Angles

Mathematics Class 11

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RD Sharma Mathematics Class 11

Mathematics Class 11 - Shaalaa.com

Chapter 4: Measurement of Angles

Ex. 4.10Others

Chapter 4: Measurement of Angles Exercise 4.10 solutions [Pages 15 - 17]

Ex. 4.10 | Q 1.1 | Page 15

Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]

Ex. 4.10 | Q 1.2 | Page 15

Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]

Ex. 4.10 | Q 1.3 | Page 15

Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]

Ex. 4.10 | Q 1.4 | Page 15

Find the degree measure corresponding to the following radian measure: 
(−3)c

Ex. 4.10 | Q 1.5 | Page 15

Find the degree measure corresponding to the following radian measure: 
 11c

Ex. 4.10 | Q 1.6 | Page 15

Find the degree measure corresponding to the following radian measure: 
 1c

Ex. 4.10 | Q 2.1 | Page 15

Find the radian measure corresponding to the following degree measure:
300°

Ex. 4.10 | Q 2.2 | Page 15

Find the radian measure corresponding to the following degree measure: 35°

Ex. 4.10 | Q 2.3 | Page 15

Find the radian measure corresponding to the following degree measure: −56°

Ex. 4.10 | Q 2.4 | Page 15

Find the radian measure corresponding to the following degree measure: 135°

Ex. 4.10 | Q 2.5 | Page 15

Find the radian measure corresponding to the following degree measure: −300°

Ex. 4.10 | Q 2.6 | Page 15

Find the radian measure corresponding to the following degree measure: 7° 30'

Ex. 4.10 | Q 2.7 | Page 15

Find the radian measure corresponding to the following degree measure: 125° 30'

Ex. 4.10 | Q 2.8 | Page 15

Find the radian measure corresponding to the following degree measure: −47° 30'

Ex. 4.10 | Q 3 | Page 15

The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.

 

 

Ex. 4.10 | Q 4 | Page 15

One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.

Ex. 4.10 | Q 5 | Page 17

If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is

  • 22 : 13

  • 11 : 13

  • 22 : 15

  • 21 : 13

Ex. 4.10 | Q 5.1 | Page 15

Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.

Ex. 4.10 | Q 5.2 | Page 15

Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.

Ex. 4.10 | Q 5.3 | Page 15

Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.

Ex. 4.10 | Q 5.4 | Page 15

Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.

Ex. 4.10 | Q 6 | Page 15

Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are

\[60^\circ, 80^\circ, 100^\circ\text{ and }120^\circ\], respectively.
Angles of the quadrilateral in radians =
\[\left( 60 \times \frac{\pi}{180} \right), \left( 80 \times \frac{\pi}{180} \right) , \left( 100 \times \frac{\pi}{180} \right) \text{ and }\left( 120 \times \frac{\pi}{180} \right)\]
\[\frac{\pi}{3}, \frac{4\pi}{9}, \frac{5\pi}{9}\text{ and } \frac{2\pi}{3}\]
 

 

Ex. 4.10 | Q 7 | Page 15

The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.

 
Ex. 4.10 | Q 8 | Page 15

The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.

 
Ex. 4.10 | Q 9 | Page 15

The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.

Ex. 4.10 | Q 10 | Page 15

The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.

 
Ex. 4.10 | Q 11 | Page 15

A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?

 
Ex. 4.10 | Q 12 | Page 15

Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.

 
Ex. 4.10 | Q 13 | Page 15

A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?

 
Ex. 4.10 | Q 14.1 | Page 15

Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length  10 cm

Ex. 4.10 | Q 14.2 | Page 15

Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length 15 cm

Ex. 4.10 | Q 14.3 | Page 15

Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length 21 cm

Ex. 4.10 | Q 15 | Page 15

The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.

Ex. 4.10 | Q 16 | Page 16

A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?

 
Ex. 4.10 | Q 17 | Page 16

Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.

Ex. 4.10 | Q 18 | Page 16

Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.

 
Ex. 4.10 | Q 19 | Page 16

If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.

Ex. 4.10 | Q 20 | Page 16

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.

Chapter 4: Measurement of Angles solutions [Page 17]

Q 1 | Page 17

If D, G and R denote respectively the number of degrees, grades and radians in an angle, then 

  • \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]

     

  • \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]

     

  • \[\frac{D}{100} = \frac{G}{100} = \frac{2R}{\pi}\]

     

  • \[\frac{D}{90} = \frac{G}{100} = \frac{R}{2\pi}\]

     

Q 2 | Page 17

If the angles of a triangle are in A.P., then the measures of one of the angles in radians is

  • \[\frac{\pi}{6}\]

     

  • \[\frac{\pi}{3}\]

     

  • \[\frac{\pi}{2}\]

     

  • \[\frac{2\pi}{3}\]

     

Q 3 | Page 17

The angle between the minute and hour hands of a clock at 8:30 is

  • 80°

  • 75°

  • 60°

  • 105°

Q 4 | Page 17

At 3:40, the hour and minute hands of a clock are inclined at

  • \[\frac{2 \pi^c}{3}\]

     

  • \[\frac{7 \pi^c}{12}\]

     

  • \[\frac{13 \pi_c}{18}\]

     

  • \[\frac{13 \pi_c}{4}\]

     

Q 6 | Page 17

If OP makes 4 revolutions in one second, the angular velocity in radians per second is

  • π

  • 2 π

  • 4 π

  • 8 π

Q 7 | Page 17

A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is

  • 50°

  • 210°

  •  100°

  • 60°

  • 195°

Q 8 | Page 17

The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\]  radian at the centre is

 
  • 10 cm

  • 20 cm

  • \[11\frac{1}{4}cm\]

     

  • \[22\frac{1}{2}cm\]

     

Chapter 4: Measurement of Angles

Ex. 4.10Others

RD Sharma Mathematics Class 11

Mathematics Class 11 - Shaalaa.com

RD Sharma solutions for Class 11 Mathematics chapter 4 - Measurement of Angles

RD Sharma solutions for Class 11 Maths chapter 4 (Measurement of Angles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 4 Measurement of Angles are Transformation Formulae, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications, 180 Degree Plusminus X Function, 2X Function, 3X Function, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, Concept of Angle, Introduction of Trigonometric Functions, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Truth of the Identity, Negative Function Or Trigonometric Functions of Negative Angles, 90 Degree Plusminus X Function, Conversion from One Measure to Another, Graphs of Trigonometric Functions.

Using RD Sharma Class 11 solutions Measurement of Angles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

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