Question

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

Explanation:

Step1: Convert degrees to radians

We know that to use the arc - length formula $s = r\theta$ (where $\theta$ is in radians), we need to convert $\theta = 102^{\circ}$ to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 102\times\frac{\pi}{180}=\frac{17\pi}{30}$ radians.

Step2: Apply the arc - length formula

The arc - length formula is $s = r\theta$. Given $r = 2$ and $\theta=\frac{17\pi}{30}$, we substitute these values into the formula: $s=2\times\frac{17\pi}{30}=\frac{17\pi}{15}$.

Answer:

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