Question

find the length of the arc s in the figure. (assume r = 2 and θ = 102°.) s =

Explanation:

Step1: Convert angle to radians

First, convert $\theta = 102^{\circ}$ to radians. Use the conversion factor $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So $\theta = 102\times\frac{\pi}{180}=\frac{17\pi}{30}$ radians.

Step2: Apply arc - length formula

The formula for the arc - length of a circle is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Given $r = 2$ and $\theta=\frac{17\pi}{30}$, then $s=2\times\frac{17\pi}{30}=\frac{17\pi}{15}\approx 3.56$.

Answer:

$\frac{17\pi}{15}$