Question

How do I find the value of theta given to area of the sector and the radius

Answer 1

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=24\\ A=90 \end{cases}\implies 90=\cfrac{\theta \pi 24^2}{360}\implies 90=\cfrac{\theta \pi 576}{360} \\\\\\ 90=\cfrac{8\theta \pi }{5}\implies 450=8\theta \pi \implies \cfrac{450}{8\pi }=\theta \implies \cfrac{225}{4\pi }=\theta \\\\\\ 17.904931 \approx \theta$