Q. 75 - 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.

$r=5$ miles,        $s=3$ miles,           $\theta =?$

Step-by-Step Solution

Answer

The required central angle $\theta =0.6 radians$.

Step 1. Given information

$r=5 miles , s=3 miles, \theta =?$

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, 

$r=5 miles and s=3 miles$

Now,

The length s of the arc is

$s=r\theta$

$\Rightarrow \theta =\frac{s}{r}$

$$\begin{gathered} \Rightarrow \theta =\frac{3}{5} \\ \Rightarrow \theta =0.6 radians \end{gathered}$$