Question

The radius of a circle is 10 miles. What is the length of a 90° arc?

Answer 1

`\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&10\\ \theta =&90 \end{cases}\implies s=\cfrac{\pi (90)(10)}{180}\implies s=5\pi \implies s\approx 15.71`