Question

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 question 5 (5 points) write $\frac{7pi}{60}$ in degrees 210° 21° 15° 21$pi$°

Explanation:

Step1: Convert angle to radians

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta_{deg} = 21^{\circ}$, then $\theta_{rad}=\frac{21\pi}{180}=\frac{7\pi}{60}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Given $r = 3$ feet and $\theta=\frac{7\pi}{60}$ radians, then $s=3\times\frac{7\pi}{60}=\frac{7\pi}{20}$ feet.

For the second part:

Step1: Convert radians to degrees

We use the formula $\theta_{deg}=\frac{180}{\pi}\times\theta_{rad}$. Given $\theta_{rad}=\frac{7\pi}{60}$, then $\theta_{deg}=\frac{180}{\pi}\times\frac{7\pi}{60}=21^{\circ}$

Answer:

First question: $s=\frac{7}{20}\pi$ feet
Second question: $21^{\circ}$