Question

the radius of the circle shown below is 9 inches. what is the approximate length of $overline{de}$? 145° a. 22.8 in b. 56.5 in c. 11.4 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 $\theta_{deg}=145^{\circ}$, then $\theta_{rad}=145\times\frac{\pi}{180}=\frac{29\pi}{36}$ radians.

Step2: Substitute values into arc - length formula

The radius $r = 9$ inches. Substitute $r = 9$ and $\theta=\frac{29\pi}{36}$ into the arc - length formula $s=r\theta$. So $s = 9\times\frac{29\pi}{36}=\frac{29\pi}{4}$.

Step3: Approximate the value

We know that $\pi\approx3.14$. Then $s=\frac{29\times3.14}{4}=\frac{91.06}{4}=22.765\approx22.8$ inches.

Answer:

A. 22.8 in