Q. 77 - 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.

$r=2$ inches,         $\theta =30°$,          $s=?$

Step-by-Step Solution

Answer

The required length s of the arc is $1.05 inches.$

Step 1. Given information

$r=2 inches, \theta =30° , s=?$

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,

$r=2 inches and \theta =30°$

We know, $\theta =30°=\frac{\mathrm{\pi }}{6}$radians

Now,

The length s of the arc is

$s=r\theta$   

$\Rightarrow s=2\times \frac{\mathrm{\pi }}{6}$

$\Rightarrow s\approx 1.05 inches$