Chapter 4, Problem 15RE

To determine

Tofind:the length of the arc on a circle of radius 20 inches intercepted by the ${138}^0$ .

Answer to Problem 15RE

The length of the arc on circle is $\text{48}\text{.171inch}$ .

Explanation of Solution

Given:The circle has a radius of 20 inches, with the central angle ${138}^0.$

Concept used:

$\text{angle=}\frac{\text{arc}}{\text{radius}}$ OR $\text{θ=}\frac{\text{l}}{\text{r}}$

Trigonometric formula:

  ${\text{πradian=180}}^{\text{0}}$

  $\text{1radian=}\frac{{\text{180}}^{\text{0}}}{\text{π}}$

or

  $1^0=1\left(\frac{\pi }{180}\right)\text{radians}$

Calculation:

Let’s consider that the circle has a radius of 20 inches, with the central angle ${138}^0.$

Let’s first convert the degree measure into radian measure, therefore,

  ${138}^0=138\left(\frac{\pi }{180}\right)$

  $\Rightarrow \frac{23\pi }{30}$

By using the formula $\text{s=rθ}$

  $\text{s=rθ}$

  $\Rightarrow \text{20}\left(\frac{23\pi }{30}\right)$

  $\Rightarrow \text{48}\text{.171inch}$

Hence, the length of the arc on circle is $\text{48}\text{.171inch}$ .