Question

What is the degree measure of an arc 4 πft? long in a circle of radius 10 ft.?

Answer 1

Answer: 36

Explanation:

Answer 2

The length of an arc is given by the formula:

`\begin{gathered} L_{\text{arc}}=(\theta)/(360)*2\pi r \\ \theta\colon\text{angular measure in degr}ee \\ r\colon\text{radius} \end{gathered}`

We are provided with the following;

`\begin{gathered} L_{\text{arc}}=4\pi\text{ ft} \\ r=10ft \end{gathered}`

Thus, we have:

`\begin{gathered} 4\pi=(\theta)/(360)*2\pi*10 \\ 4\pi*360=\theta*20\pi \\ (4\pi*360)/(20\pi)=\theta \\ \theta=72^0 \end{gathered}`

Hence, the degree measure is 72 degrees