Question

A circle has a radius of 48 millimeters. What is the central angle in radians, that intercepts an arc of length 36π millimeters?

Answer 1

Arc length= radius x angle
36pie=48 x angle
divide both side by 48
you get 3/4pie

Answer 2

Answer:

$\theta=\dfrac{3\pi}{4}$

Step-by-step explanation:

The formula for length of intercepted arc is

$s=r\theta$

where, r is the radius of the circle and θ in the central angle in radian.

Radius of the circle = 48 millimeters

Length of intercepted arc = 36π millimeters

Substitute the given values in the above formula.

$36\pi=48\theta$

Divide both sides by 48.

$\dfrac{36\pi}{48}=\dfrac{48\theta}{48}$

$\dfrac{3\pi}{4}=\theta$

Therefore, the measure of central angle is $\theta=\dfrac{3\pi}{4}$.