Question

the radius of a circle is 5 centimeters. what is the length of a 45° arc?
give the exact answer in simplest form.
centimeters

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Substitute the given values into the formula

Given \(\theta = 45^{\circ}\) and \(r = 5\) cm.

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Answer:

\(\frac{5\pi}{4}\)