Q. 73 - 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. 

$\theta =\frac{1}{3}$ radian,       $s=2$ feet ,      $r=?$

Step-by-Step Solution

Answer

The radius of the circle is $6 feet.$

Step 1. Given information

$\theta =\frac{1}{3} radians , s=2 feet, r=?$

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,

$\theta =\frac{1}{3}radian and s=2 feet$

The length $s$ of the arc is

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

$\Rightarrow r=\frac{2}{{\displaystyle \frac{1}{3}}}$

$\Rightarrow r=6 feet$