Question

the radius of a circle is 15. what is the length of an arc that subtends an angle of \frac{\pi}{8} radians? give the exact answer in simplest form.

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) of a circle is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 15\) and \(\theta=\frac{\pi}{8}\). Then \(s=15\times\frac{\pi}{8}\).

Answer:

\(\frac{15\pi}{8}\)