Question

What is the measure of the ARC length the ARC in bold

Answer 1

Given

radius = 9 yd

First, convert the given angle of the arc length into radians

`\begin{gathered} \theta=240°\cdot(\pi)/(180°) \\ \theta=(4)/(3)\pi \end{gathered}`

Next, solve for the arc length using the formula

`\begin{gathered} s=r\theta \\ \text{where} \\ r\text{ is the radius} \\ s\text{ is the arc length} \end{gathered}`

Substitute y = 9 yd and we get

`\begin{gathered} s=r\theta \\ s=(9\text{ yd})((4\pi)/(3)) \\ s=(36\pi)/(3)\text{ yd} \\ s=12\pi\text{ yd} \\ \\ \text{Therefore, the arc length is equal to }12\pi\text{ yd}. \end{gathered}`