Chapter 7.4, Problem 43E

To determine

To find: the degree measure to the nearest tenth of the central angle of a circle.

Answer to Problem 43E

  $97.4°$

Explanation of Solution

Given information:

  $\begin{array}{l}s=17\text{ cm}\end{array}$

  $\begin{array}{c}r=10\text{ cm}\end{array}$

Calculation:

The value of central angle $\left(\theta \right)$ can be evaluated as follows:

  $\begin{array}{c}s=r\theta \end{array}$

  $\begin{array}{c}17=\left(10\right)\theta \left[\text{Put the value of }s\text{ and }r\right]\end{array}$

  $\begin{array}{c}\theta =\frac{17}{10}\end{array}$

  $\begin{array}{c}=1.7\text{ radians}\end{array}$

  $\begin{array}{c}\text{=1}\text{.7 }\left(\frac{180°}{\pi }\right)\left[\text{Change into degree measure}\right]\end{array}$

  $\begin{array}{c}=97.4°\end{array}$

Thus the value of central angle in degree measure is $97.4°$ .