Question

A circle has a radius of 13cm . Find the radian measure of the central angle 0 that intercepts an arc of length8cm . Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

The measure of the center angle is 0.6 radians

Explanation:

Mathematically, the length of an arc can be calculated using;

L = theta/360 * 2 * pi * r

where theta is the central angle

In this case, theta = ? , pi = 22/7 and r is 13

cm, length of arc is 8 cm

So we have ;

8 = theta/360 * 2 * pi * 13

360 * 7 * 8 = theta * 2 * 22 * 13

20,160 = 572 theta

theta = 20,160/572

theta = 35.24

let us convert this to radian measure

Mathematically, 1 degree = 0.0175 radian

Thus 35.24 degrees will be 35.24 * 0.0175 = 0.62 radians

To the nearest tenth, this is 0.6 radians