Question

What is the angle in both radians and degrees determined by an arc of length 2pi meters on a circle of radius 8 meters?

Answer 1

$\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta = angle~in\\ \qquad radians\\ ------\\ r=18\\ s=2\pi \end{cases}\implies 2\pi =18\theta \implies \cfrac{2\pi }{18}=\theta\implies \cfrac{\pi }{9}=\theta \\\\ -------------------------------$

$\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta = angle~in\\ \qquad degrees\\ ------\\ r=18\\ s=2\pi \end{cases}\implies 2\pi =\cfrac{\theta \pi 18}{180} \\\\\\ 2\pi =\cfrac{\theta \pi }{10}\implies \cfrac{2\pi (10)}{\pi }=\theta \implies 20=\theta$