Question

Does anybody know this? An arc has a length of 30 pi feet. Find tge length of the radius if the central angle measured 225

Answer 1

$\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=30\pi \\ \theta =225 \end{cases}\implies 30\pi =\cfrac{(225)\pi r}{180} \\\\\\ 30\pi (180)=225\pi r\implies \cfrac{30\pi (180)}{225\pi }=r\implies 24=r$