Question

A circle has a radius of 19 m. Find the radian measure of the central angle θ that intercepts an arc of length 16m. Do not round any intermediate computations, and round your answer to the nearest tenth.θ= __ radians

Answer 1

Shinshia, this is the solution:

Radius of a circle = 19 m

Arc of Length = 16 m

In consequence, we have:

Arc Length = Central angle/360 * Circumference

Replacing by the values we know:

16 = Central angle/360 * 2 * π * r

16 = Central angle/360 * 38π

360 * 16 = Central angle * 38π

5,760 = Central angle * 38π

Central angle = 5,760/38π

Central angle = 48.25 degrees

Converting to radians, we have:

48.25 * π/180

0.8421

0.8 radians (rounding to the nearest tenth)