Answer
$\frac{6}{\pi}\approx1.91$ km
Work Step by Step
We know that the length of the arc $s$ cut off by $\theta$ can be calculated as $s=r\theta$. Therefore, we also know that $r=\frac{s}{\theta}$.
We are given that $\theta=150^{\circ}$ and $s=5$ km.
We can convert $\theta$ to radians by multiplying $\theta$ by $\frac{\pi}{180}$.
$\theta=150^{\circ}=150(\frac{\pi}{180})=\frac{150\pi}{180}=\frac{5\pi}{6}$
Therefore, $r=\frac{5}{\frac{5\pi}{6}}=5\times\frac{6}{5\pi}=\frac{5\times6}{5\pi}=\frac{30}{5\pi}=\frac{30\div5}{5\pi\div5}=\frac{6}{\pi}\approx1.91$ km.
