Chapter 6.1, Problem 39E

To determine

To find: the length intercepted arc in a circle, round to the nearest tenth.

Answer to Problem 39E

78.2 cm

Explanation of Solution

Given information:

  $\begin{array}{c}\text{Central angle}\left(\theta \right)=320°\\ \text{Radius}\left(r\right)=14\text{ cm}\end{array}$

Calculation:

Convert degree into radian by multiplying the degree by $\frac{\pi }{180°}$ as shown below.

  $\begin{array}{c}\theta =320°\left(\frac{\pi }{180°}\right)\\ =\frac{80\pi }{45}\end{array}$

Now evaluate the length of arc $\left(s\right)$ as follows:

  $\begin{array}{c}s=r\theta \\ =14\left(\frac{80\pi }{45}\right)\left[\text{Put the value of }r\text{ and }\theta \right]\\ =24.9\pi \\ =78.2\text{ cm}\end{array}$

Thus the length of arc is 78.2 cm.