Question

find the arc length, s, if r = 11 and the measure of the angle, \\( \theta = \frac { 12 \pi } { 13 } \\) radians. s = \\( \frac { ? \pi } { } \\)

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values

Given \(r = 11\) and \(\theta=\frac{12\pi}{13}\), substitute into the formula: \(s=11\times\frac{12\pi}{13}\).

Step3: Calculate the value

\(s=\frac{132\pi}{13}\)

Answer:

\(\frac{132\pi}{13}\)