Question

the radius of a circle is 2 miles. what is the length of a 45° arc?

r=2 mi
45°

give the exact answer in simplest form.

miles
π
\frac{□}{□}

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc with central angle \(\theta\) (in degrees) in a circle of radius \(r\) is \(L=\frac{\theta}{360^\circ}\times2\pi r\). Here, \(\theta = 45^\circ\) and \(r = 2\) miles.

Step2: Substitute values into formula

Substitute \(\theta = 45^\circ\) and \(r = 2\) into the formula: \(L=\frac{45^\circ}{360^\circ}\times2\pi\times2\).
Simplify \(\frac{45}{360}=\frac{1}{8}\), so \(L=\frac{1}{8}\times4\pi\).
Simplify \(\frac{1}{8}\times4\pi=\frac{4\pi}{8}=\frac{\pi}{2}\).

Answer:

\(\frac{\pi}{2}\)