Chapter 4.1, Problem 51E

To determine

The length of the arc.

Answer to Problem 51E

The length of the arc is 31.42 inches

Explanation of Solution

Given information:Radius $r=15in$ , central angle $\theta ={120}^0$

Concept used:

The length of the arc of a circle with radius $r$ and central angle $\theta$ (in radians) is $s=r\theta$

Calculation:

Given central angle $\theta ={120}^0$

Convert into radians

  $\begin{array}{l}\theta ={120}^0=120(\frac{\pi }{180})rad\\ \theta =\frac{2\pi }{3}rad\end{array}$

Put $r=15in$ , $\theta =\frac{2\pi }{3}rad$ in $s=r\theta$

  $\begin{array}{l}s=15(\frac{2\pi }{3})=10\pi \\ s=31.42in\end{array}$

Therefore the length of the arc is 31.42 inches