Question

find the length s of the arc of a circle of radius 80 centimeters subtended by the central angle 72°. s (arc length) = centimeters (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Convert angle to radians

First, convert $72^{\circ}$ to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, $\theta = 72\times\frac{\pi}{180}=\frac{2\pi}{5}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Given $r = 80$ cm and $\theta=\frac{2\pi}{5}$ radians. Then $s=80\times\frac{2\pi}{5}$.

Step3: Calculate the arc - length

$s = 80\times\frac{2\pi}{5}=32\pi\approx32\times 3.14159 = 100.531$ cm.

Answer:

$100.531$