Class 11th Maths – RD Sharma Chapter 4 : Measurement Of Angles Exercise 4.1 Solutions
- Find the degree measure corresponding to the following radian measures (Use π = 22/7) :
(i) 9π/5 Watch Solution
(ii) − 5π/6 Watch Solution
(iii) (18π/5)^c Watch Solution
(iv) (− 3)^c Watch Solution
(v) 11^c Watch Solution
(vi) 1^c Watch Solution - Find the radian measure corresponding to the following degree measures:
(i) 300° Watch Solution
(ii) 35° Watch Solution
(iii) − 56° Watch Solution
(iv) 135° Watch Solution
(v) − 300° Watch Solution
(vi) 7° 30′ Watch Solution
(vii) 125° 30′ Watch Solution
(viii) − 47° 30′ Watch Solution - The difference between the two acute angles of a right-angled triangle is 2π/5 radians. Express the angles in degrees. Watch Solution
- One angle of a triangle is 2/3 x grades and another is 3/2 x degrees while the third is πx/75 radians. Express all the angles in degrees. Watch Solution
- Find the magnitude, in radians and degrees, of the interior angle of a regular
(i) pentagon Watch Solution
(ii) octagon Watch Solution
(iii) heptagon Watch Solution
(iv) duodecagon. Watch Solution - The angles of a quadrilateral are in A.P. and the greatest angle is 120°. Express the angles in radians. Watch Solution
- 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. Watch Solution
- 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. Watch Solution
- The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians. Watch Solution
- 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. Watch Solution
- 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? Watch Solution
- Find the length which at a distance of 5280 m will subtend an angle of 1′ at the eye. Watch Solution
- A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second? Watch Solution
- Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
(i) 10 cm Watch Solution
(ii) 15 cm Watch Solution
(iii) 21 cm. Watch Solution - 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. Watch Solution
- 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? Watch Solution
- 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′. Watch Solution
- 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 × 10^6 km. Watch Solution
- If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii. Watch Solution
- 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 (Use π = 22/7). Watch Solution