If a denotes the length of the arc of a circle of radius r by a central angle theata, find the missing quantity of r. Include units.

Question

R=?, theata=pi/13, s=7cm

please give full answer

Answer 1

arc length = radius time the angle measured in radians

s = r(theta)

r = s/theta = 7 cm/pi/13 = 7(13)/pi

= 81/pi

= about 25.78 cm = radius

radius = arc length divided by theta (measured in radians)

pi/13 is a relatively small angle, = about 13.85 degrees. a

larger radius correlates with a smaller arc length given the small angle