Question

The radius of a circle is 5 meters. What is the angle measure of an arc 3pi meters long?

Answer 1

The arc length angle relation is given by,

`l=r\theta`

Here, l is the arc length, r is the radius of the circle and θ is the central angle of the arc.

Given, l=3π m and r =5 m. Put values of l and r in above equation and find θ.

`\begin{gathered} 3\pi\text{ =5}*\theta \\ (3\pi)/(5)=\theta \\ 0.6\pi=\theta \end{gathered}`

The angle measure of the arc is 0.6π radians.

In degrees,

`\begin{gathered} \theta_d=\theta*(180^(\circ))/(\pi) \\ =0.6\pi*(180^(\circ))/(\pi) \\ =108^(\circ) \end{gathered}`

In degrees, the angle measure of arc is 108 degrees.