Question

arc ef subtends central angle θ. if the length of arc ef equals 30 inches, and central angle θ equals 2.5 radians, what is the measure of radius r? use the keypad to enter your answer in the box. the radius, r, equals inches.

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius, and $\theta$ is the central angle in radians.

Step2: Solve for radius $r$

We are given that $s = 30$ inches and $\theta=2.5$ radians. Rearranging the formula $s = r\theta$ for $r$, we get $r=\frac{s}{\theta}$.
Substitute $s = 30$ and $\theta = 2.5$ into the formula: $r=\frac{30}{2.5}$.
$r = 12$ inches.

Answer:

12