Q. 78 - Precalculus Enhanced with Graphing Utilities

Question

In the problem, $s$ denotes the length of the arc of a circle of radius $r$ subtended by the central angle $\theta$ . Find the missing quantity. Round answers to three decimal places.

$r=3$ meters,       $\theta =120°$,        $s=?$

Step-by-Step Solution

Answer

The required length s of the arc is $6.28$ meters.

Step 1. Given information

$r=3 meters, \theta =120° and s=?$

Step 2. Formula Used

For a circle of radius $r$ , a central angle of $\theta$ radians subtends an arc whose length $s$ is

          $s=r\theta$

Step 3. Calculation

We have, 

$r=3 meters and \theta =120°=120\times \frac{\mathrm{\pi }}{180°}=2.093 radians$

Now,

The length s of the arc is

$s=r\theta$

$\Rightarrow s=3\times 2.093$

$\Rightarrow s\approx 6.28$ meters