Question

find the length of the darkened arc.
circle with radius 17 mi, central angle 165° for the darkened arc, multiple - choice options: $\frac{125}{8}pi$, $\frac{187}{12}pi$, $24pi$, $\frac{3179}{24}pi$

Explanation:

Step1: Recall arc length formula

The formula for arc length $L$ is $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle and $r$ is the radius.

Step2: Substitute given values

Here, $\theta = 165^\circ$, $r = 17$ mi.
$L = \frac{165^\circ}{360^\circ} \times 2\pi \times 17$

Step3: Simplify the expression

First simplify $\frac{165}{360} = \frac{11}{24}$, then calculate $2 \times 17 = 34$.
$L = \frac{11}{24} \times 34\pi = \frac{374}{24}\pi = \frac{187}{12}\pi$

Answer:

B. $\frac{187}{12}\pi$