Question

question 8 (5 points)
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for a circle of radius 3 feet, find the arc length s subtended by a central angle of 21°.
( s=\frac{7}{40}pi ) feet
( s=\frac{7}{20}pi ) feet
( s=\frac{7}{5}pi ) feet
( s=\frac{7}{10}pi ) feet

Explanation:

Step1: Convert degree to radian

The formula to convert degrees to radians is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$.
Given $\theta = 21^{\circ}$, then $\theta_{rad}=21\times\frac{\pi}{180}=\frac{7\pi}{60}$ 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 $r = 3$ feet and $\theta=\frac{7\pi}{60}$, then $s=3\times\frac{7\pi}{60}$.
Simplify $3\times\frac{7\pi}{60}=\frac{7\pi}{20}$ feet.

Answer:

$s=\frac{7}{20}\pi$ feet (the second option)