Q. 76 - 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. 

$r=6$ meters,         $s=8$ meters,        $\theta =?$

Step-by-Step Solution

Answer

The required central angle $\theta =1.33 radians$

Step 1. Given information

$r=6 meters , s=8 meters , \theta =?$

Step 2. Formula Used

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

             $s=r\theta$

Step 3. Calculation

We have, 

$r=6 meters and s=8 meters$

Now,

The length s of the arc is

$$\begin{gathered} s=r\theta \\ \Rightarrow \theta =\frac{s}{r} \end{gathered}$$

$$\begin{gathered} \Rightarrow \theta =\frac{8}{6} \\ \Rightarrow \theta =1.33 radians \end{gathered}$$