Question

120° 4 in. s

Explanation:

Step1: Convert angle to radians

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 120^{\circ}$, then $\theta_{rad}=120\times\frac{\pi}{180}=\frac{2\pi}{3}$.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Here, $r = 4$ inches and $\theta=\frac{2\pi}{3}$. So $s=4\times\frac{2\pi}{3}=\frac{8\pi}{3}\approx8.38$ inches.

Answer:

$\frac{8\pi}{3}\text{ inches}\approx8.38\text{ inches}$