Question

What is the measure of the central angle that intercepts an Arc that has a length of 5.45 m and a radius of 2 m

Answer 1

`\bf \textit{arc's length}\\\\ s = \cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta = \stackrel{central}{angle}~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=2\\ s=5.45 \end{cases}\implies 5.45=\cfrac{\pi \theta (2)}{180}\implies 5.45=\cfrac{\theta \pi }{90} \\\\\\ 490.5=\theta \pi \implies \cfrac{490.5}{\pi }=\theta \implies \stackrel{degrees}{156.13\approx \theta }~\hfill \stackrel{radians}{2.72\approx \theta }`