Q.71 - 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.

$r=10$meters,    $\theta =\frac{1}{2}$radian,    $s=?$

Step-by-Step Solution

Answer

The required length $s$ of the arc is   $5 meters$.

Step 1. Given information

 Given, $r=10 meteres, \theta =\frac{1}{2}radian, s=?$

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,

$r=10 meters$, $\theta =\frac{1}{2}radian$,

The length $s$ of the arc is

$s=r\theta$

$\Rightarrow s=10\times \frac{1}{2}$      (given)

$\Rightarrow s=5$meters (simplify)