Answer
$\frac{35\pi}{4}\approx27.49$ in
Work Step by Step
We know that the length of the arc $s$ cut off by $\theta$ can be calculated as $s=r\theta$.
We are given that $\theta=315^{\circ}$ and $r=5$ in.
To convert $\theta$ to radians, we must multiply $\theta$ by $\frac{\pi}{180}$.
$\theta=315^{\circ}=315(\frac{\pi}{180})=\frac{315\pi}{180}=\frac{7\pi}{4}$
Therefore, $s=\frac{7\pi}{4}(5)=\frac{7\pi}{4}\times5=\frac{7\pi\times5}{4}=\frac{35\pi}{4}\approx27.49$ in.
