Question

1. find the measure of the central angle in the diagram below. 9 mi 6π mi

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify given values

We are given that $r = 9$ mi and $s=6\pi$ mi.

Step3: Solve for the central angle $\theta$

Substitute the given values into the formula $s = r\theta$. We get $6\pi=9\theta$. Then $\theta=\frac{6\pi}{9}=\frac{2\pi}{3}$ radians.

Answer:

$\frac{2\pi}{3}$ radians