Question

How do you find the lengths of the arc on a circle of radius $9\mathrm{feet}$ intercepted by the central angle $60°$?

Answer 1

Find the arc length.

We know that,

$\mathrm{Arc}\mathrm{length}=2\pi r\left(\frac{\theta }{{360}^{\circ }}\right)$, where $\theta$ is the angle in degrees and $r$ is the radius of the circle.

Substitute $r$ as $9$ and $\theta$ as $60°$ in the formula above.

$\begin{array}{rcl}\mathrm{Arc}\mathrm{length}& =& 2\pi \left(9\right)\frac{60°}{360°}\\ \Rightarrow \mathrm{Arc}\mathrm{length}& =& 18\pi \frac{60°}{360°}\\ \Rightarrow \mathrm{Arc}\mathrm{length}& =& \pi \frac{60°}{20°}\\ \Rightarrow \mathrm{Arc}\mathrm{length}& =& 3\pi \\ & \Rightarrow & \mathrm{Arc}\mathrm{length}=3\left(3.14\right)\\ \therefore \mathrm{Arc}\mathrm{length}& =& 9.42\mathrm{ft}\end{array}$

Hence, the arc length is $9.42\mathrm{ft}$.