Question

In a circle, the length of an an arc intercepted by a central angle is 12mm, and the radius of the circle is a 8 mm. What is the measure, in radians, of the angle?

Answer 1

$\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ s=12\\ r=8 \end{cases}\implies 12=8\theta \implies \cfrac{12}{8}=\theta \implies \cfrac{3}{2}=\theta$