Question

the circle below has center v, and its radius is 5 ft. given that m∠wvx=150°, find the length of the minor arc \\(\overarc{wx}\\). give an exact answer in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( s = \frac{\theta}{360^\circ} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify given values

We know that \( \theta = 150^\circ \) and \( r = 5 \) ft.

Step3: Substitute values into formula

Substitute \( \theta = 150^\circ \) and \( r = 5 \) into the arc length formula:
\( s = \frac{150^\circ}{360^\circ} \times 2\pi \times 5 \)

Step4: Simplify the expression

First, simplify \( \frac{150}{360} = \frac{5}{12} \). Then:
\( s = \frac{5}{12} \times 10\pi = \frac{50\pi}{12} = \frac{25\pi}{6} \)

Answer:

\(\frac{25}{6}\pi\) feet