Question

PLEASE HELP!The sector of a circle has a surface of 45 cm2. What is the angle of the sector, if the radius is 14.2 cm?​

Answer 1

$\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=45\\ r=14.2 \end{cases}\implies 45=\cfrac{\theta \pi (14.2)^2}{360}\implies \cfrac{45}{(14.2)^2 \pi }=\cfrac{\theta }{360} \\\\\\ \cfrac{45(360)}{(14.2)^2 \pi }=\theta \implies 25.57^o\approx \theta$