Question

A central angle of a circle measures 42°. The arc intercepted by this central angle measures 12 inches.

Which value best approximates the radius of the circle?
8.67 in.
16.37 in.
17.34 in.
32.74 in.

Answer 1

Answer:16.37 in.

Explanation:

Answer 2

`\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ s=12 \end{cases}\implies 12=\cfrac{(42)\pi r}{180}\implies 12=\cfrac{7\pi r}{30} \\\\\\ 360=7\pi r\implies \cfrac{360}{7\pi }=r\implies 16.37\approx r`