Question

find the length s of the circular arc shown in the following figure. resources read it watch it

Explanation:

Step1: Convert angle to radians

We know that to use the arc - length formula $s = r\theta$ (where $r$ is the radius and $\theta$ is the angle in radians), we need to convert $120^{\circ}$ to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 120\times\frac{\pi}{180}=\frac{2\pi}{3}$ radians.

Step2: Apply arc - length formula

The radius $r = 8$. Using the formula $s=r\theta$, we substitute $r = 8$ and $\theta=\frac{2\pi}{3}$. Then $s=8\times\frac{2\pi}{3}=\frac{16\pi}{3}$.

Answer:

$\frac{16\pi}{3}$