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 arc length formula

The formula for arc length \( s \) when the angle \( \theta \) is in radians is \( s = r\theta \).

Step2: Substitute given values

We know \( r = 11 \) and \( \theta=\frac{12\pi}{13} \). Substitute these into the formula:
\( s = 11\times\frac{12\pi}{13} \)
Simplify the multiplication: \( s=\frac{132\pi}{13} \)

Answer:

\( \frac{132}{13}\pi \) (or in the boxed form as per the question's format, the numerator is 132 and denominator is 13, so \( s = \frac{\boldsymbol{132}\pi}{\boldsymbol{13}} \))