Question

find the arc - length of a circle with the given radius $r$ and central angle $\theta$. give the answer in the given unit of measure, rounded to the nearest hundredth.
$r = 58$ m; $\theta=240^{circ}$

Explanation:

Step1: Convert angle to radians

First, convert the central - angle from degrees to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$.
$\theta = 240^{\circ}\times\frac{\pi}{180}=\frac{4\pi}{3}$ radians

Step2: Use the arc - length formula

The arc - length formula for a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius, and $\theta$ is the central angle in radians.
Given $r = 58$ m and $\theta=\frac{4\pi}{3}$, then $s=58\times\frac{4\pi}{3}=\frac{232\pi}{3}$ m.

Step3: Calculate the numerical value

Now, calculate the value of $\frac{232\pi}{3}$ and round to the nearest hundredth.
$\frac{232\pi}{3}\approx\frac{232\times3.14159}{3}\approx242.81$ m

Answer:

$242.81$ m