Question

The radius of a circle is 10 inches. What is the angle measure of an arc 3​ inches long?

Answer 1

`\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ s=3 \end{cases} \implies 3=\cfrac{\theta \pi (10)}{180}\implies 540=10\pi \theta \\\\\\ \cfrac{540}{10\pi }=\theta \implies 17.19^o\approx \theta`