Question

A circle has a radius of $19\mathrm{in}$, how do you find the radian measure of the central angle that intercepts an arc of length $9\mathrm{in}$?

Answer 1

Find the central angle.

Central angle in radians, ${\alpha }_{\mathrm{radian}}$ is given by the formula-

${\alpha }_{\mathrm{radian}}=\frac{\mathrm{arc}}{r}...\left(1\right)$

Here, the length of arc is $9\mathrm{in}$ and radius of circle is $19\mathrm{in}$.

Substituting values in equation $\left(1\right)$.

$$\begin{gathered} {\alpha }_{\mathrm{radian}}=\frac{9}{19} \\ \therefore {\alpha }_{\mathrm{radian}}\approx 0.47 \end{gathered}$$

Hence, the value of the central angle is $\mathbf{0}\mathbf{.}\mathbf{47}\mathbf{}\mathbf{radians}$.