Question

the radius of a circle is 14 meters. what is the length of an arc that subtends an angle of \\( \frac{\pi}{5} \\) radians? give the exact answer in simplest form. meters

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) 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 \(r = 14\) meters and \(\theta=\frac{\pi}{5}\) radians.
Substitute into \(s = r\theta\), we get \(s=14\times\frac{\pi}{5}\).

Answer:

\(\frac{14\pi}{5}\) meters