Question

a circular arc of length 8 ft subtends a central angle of 20°. find the radius of the circle. (round your answer to two decimal places.) ft

Explanation:

Step1: Convert angle to radians

We know that to use the arc - length formula $s = r\theta$ (where $s$ is arc - length, $r$ is radius and $\theta$ is the central angle in radians), we need to convert $20^{\circ}$ to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. So, $\theta = 20\times\frac{\pi}{180}=\frac{\pi}{9}$ radians.

Step2: Solve for radius

Given $s = 8$ ft and $\theta=\frac{\pi}{9}$ radians, from the formula $s = r\theta$, we can solve for $r$. Rearranging the formula gives $r=\frac{s}{\theta}$. Substituting the values, we have $r=\frac{8}{\frac{\pi}{9}}$.

Step3: Calculate the value of radius

$r=\frac{8\times9}{\pi}=\frac{72}{\pi}\approx22.92$ ft.

Answer:

$22.92$