Question

the radius of a circle is 5 miles. what is the angle measure of an arc π miles long?
l=π ml
r=5 mi
give the exact answer in simplest form.

Explanation:

Step1: Recall the arc - length formula

The formula for the arc - length \(l\) of a circle is \(l=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.
We are given that \(l = \pi\) miles and \(r = 5\) miles.
Substitute these values into the formula: \(\pi=\frac{\theta}{360}\times2\pi\times5\).

Step2: Solve for \(\theta\)

First, divide both sides of the equation \(\pi=\frac{\theta}{360}\times10\pi\) by \(\pi\) (since \(\pi
eq0\)).
We get \(1=\frac{\theta}{360}\times10\).
Then, multiply both sides by \(\frac{360}{10}\).
\(\theta=\frac{360\times1}{10}\).

Answer:

\(36\)