Question

find the length s of the arc of a circle of radius 10 centimeters subtended by the central angle 24°. s (arc length) = centimeters (type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Convert angle to radians

First, convert $24^{\circ}$ to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 24\times\frac{\pi}{180}=\frac{2\pi}{15}$ 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 $r = 10$ cm and $\theta=\frac{2\pi}{15}$ radians, then $s=10\times\frac{2\pi}{15}=\frac{4\pi}{3}\approx4.189$ cm.

Answer:

$4.189$