Question

find the length s of the arc of a circle of radius 25 feet subtended by the central angle 39°. s (arc length)= feet (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Convert angle to radians

First, convert $39^{\circ}$ to radians. We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 39\times\frac{\pi}{180}=\frac{13\pi}{60}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Given $r = 25$ feet and $\theta=\frac{13\pi}{60}$ radians. Then $s=25\times\frac{13\pi}{60}=\frac{65\pi}{12}\approx 17.027$ feet.

Answer:

$17.027$