Question

Need help please .The ares of the sector shown below is 59 yd^2 find the length of the radius. Round to the nearest whole number use 3.14 for pi

Answer 1

$\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=59\\ \theta =40 \end{cases}\implies 59=\cfrac{(40)\pi r^2}{360}\implies 59(360)=40\pi r^2 \\\\\\ \cfrac{59(360)}{40\pi }=r^2\implies \cfrac{531}{\pi }=r^2\implies \sqrt{\cfrac{531}{\pi }}=r\implies 13\approx r$