Question

Use the formula for radian measure to calculate the measure of the central angle of a circle with a radius $12\mathrm{cm}$ intercepting an arc of $21\mathrm{cm}$.

Answer 1

Finding the measure of the central angle of the circle using Radian Measure Formula :

Let $\theta$ denote the central angle of the circle.

Let $r$ denote the radius of the circle.

According to the formula, $\theta =\frac{\mathrm{Arc}\mathrm{length}}{r}\mathrm{radian}$

Calculate the measure of the central angle as shown:

$$\begin{gathered} \theta =\frac{21}{12}\mathrm{radian} \\ \theta =1.75\mathrm{radian} \end{gathered}$$

Therefore, the measure of the central angle of the circle is $1.75\mathrm{radian}$.