Question

circle c has a radius of 42 feet. the measure of ∠acb is $\frac{2pi}{3}$ radians. what is the length of arc ab? write an exact, simplified answer. do not round. feet

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.

Step2: Identify values of $r$ and $\theta$

Given that $r = 42$ feet and $\theta=\frac{2\pi}{3}$ radians.

Step3: Substitute values into formula

$s=42\times\frac{2\pi}{3}$.

Step4: Simplify the expression

$42\times\frac{2\pi}{3}=\frac{42\times2\pi}{3}=\frac{84\pi}{3}=28\pi$ feet.

Answer:

$28\pi$