Question

How do you find the radian measure of the central angle of a circle of radius $8\mathrm{feet}$ that intercepts an arc of length $14\mathrm{feet}$ ?

Answer 1

Use the relation between radius, arc length, and radian measure to find the unknown radian measure

The relation can be given as:

$\mathrm{\theta }=\frac{\mathrm{arc}\mathrm{length}}{\mathrm{radius}}$

Where $\theta$ is in radian

Substituting the values:

$$\begin{gathered} \Rightarrow \theta =\frac{14}{8} \\ \Rightarrow \theta =\frac{7}{4} \end{gathered}$$

Therefore, The radian measure of the central angle is $\frac{\mathbf{7}}{\mathbf{4}}$.