Question

how long is an arc intercepted by the given central angle in a circle of radius 12.55 mi? 150° the length of the intercepted arc is approximately mi. (round to the nearest hundredth.)

Explanation:

Step1: Convert angle to radians

First, convert $150^{\circ}$ to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, $150^{\circ}=150\times\frac{\pi}{180}=\frac{5\pi}{6}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $s$ is the arc length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. Given $r = 12.55$ mi and $\theta=\frac{5\pi}{6}$, then $s=12.55\times\frac{5\pi}{6}$.

Step3: Calculate the value

$s = 12.55\times\frac{5\pi}{6}\approx12.55\times\frac{5\times3.14159}{6}\approx12.55\times2.61799\approx32.86$ mi

Answer:

$32.86$