Question

the circumference of the circle shown below is 75 inches. which expression gives the length in inches of $widehat{de}$?
a. $\frac{72}{360}cdot75pi$
b. $\frac{360}{72}cdot75pi$
c. $\frac{72}{360}cdot75$
d. $\frac{360}{72}cdot75$

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s=\frac{\theta}{360}\times C$, where $\theta$ is the central - angle measure of the arc in degrees and $C$ is the circumference of the circle.

Step2: Identify given values

We are given that $\theta = 72^{\circ}$ and $C = 75$ inches.

Step3: Substitute values into formula

Substituting $\theta = 72$ and $C = 75$ into the arc - length formula $s=\frac{\theta}{360}\times C$, we get $s=\frac{72}{360}\times75$.

Answer:

C. $\frac{72}{360}\cdot75$