Question

A circle has a radius if 20 centimeters and a central angle that measures 118 degrees. Find the length of the arc defined by thus central angle

Answer 1

$\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =118 \end{cases}\implies \begin{array}{llll} s=\cfrac{(118)\pi (20)}{180}\implies s=\cfrac{118\pi }{9} \\\\\\ s\approx 41.19~cm \end{array}$