Question

finding arc length in exercises 51 and 52, find the length of the arc on a circle of radius r intercepted by a central angle θ. 51. r = 15 inches, θ = 120.

Explanation:

Step1: Convert angle to radians

First, convert $\theta = 120^{\circ}$ to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, $\theta=120\times\frac{\pi}{180}=\frac{2\pi}{3}$ radians.

Step2: Use arc - length formula

The formula for the arc - length $s$ of a circle is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Given $r = 15$ inches and $\theta=\frac{2\pi}{3}$ radians. Then $s=15\times\frac{2\pi}{3}$.

Step3: Calculate the arc - length

$s = 10\pi\approx 10\times 3.14 = 31.4$ inches.

Answer:

$10\pi\approx31.4$ inches