Question

the radius of the circle shown below is 7 inches. what is the approximate length of $widehat{ab}$? 135° a b a. 8.2 in b. 16.5 in

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians. First, convert the angle from degrees to radians. We know that to convert degrees to radians, we use the conversion factor $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg}=135^{\circ}$, then $\theta_{rad}=135\times\frac{\pi}{180}=\frac{3\pi}{4}$ radians, and $r = 7$ inches.

Step2: Calculate the arc - length

Substitute $r = 7$ and $\theta=\frac{3\pi}{4}$ into the arc - length formula $s=r\theta$. So $s = 7\times\frac{3\pi}{4}=\frac{21\pi}{4}\approx\frac{21\times3.14}{4}=\frac{65.94}{4}=16.485\approx16.5$ inches.

Answer:

B. 16.5 in