Question

In a circle with radius 8, an angle intercepts an are of length 23. Find the angle in

radians in simplest form.

Answer 1

`\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=8\\ s=(20\pi )/(3) \end{cases}\implies \cfrac{20\pi }{3}=8\theta \implies \cfrac{20\pi }{24}=\theta \implies \cfrac{5\pi }{6}=\theta`