Question

On a circle of radius $10$ feet, what angle would subtend an arc of length $3$ feet?

Answer 1

Determine the angle.

The length of an arc is given by the formula $s=r\theta$, where $\theta$ is in radians.

Here, $s=3\mathrm{and}r=10$.

Determine the value of the angle:

$\begin{array}{rcl}3& =& 10\theta \\ & \Rightarrow & \theta =\frac{10}{3}\mathrm{radians}\end{array}$

Convert the angle in radians to degrees:

$\begin{array}{rcl}\theta & =& \frac{10}{3}\times \frac{360°}{2\pi }\\ & \Rightarrow & \theta =\left(\frac{600°}{\pi }\right)\end{array}$

Hence, the angle is $\frac{600°}{\pi }$.