Question

the circle below has center k, and its radius is 3 yd. given that ( mangle lkm = 60^circ ), find the length of the minor arc ( overarc{lm} ). give an exact answer in terms of ( pi ), and be sure to include the correct unit in your answer. length of minor arc ( overarc{lm} ) :

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc with central angle \(\theta\) (in degrees) and radius \(r\) is \(s=\frac{\theta}{360^\circ}\times2\pi r\).

Step2: Identify given values

Here, \(\theta = 60^\circ\) and \(r = 3\) yd.

Step3: Substitute values into formula

Substitute \(\theta = 60^\circ\) and \(r = 3\) into the formula:
\(s=\frac{60^\circ}{360^\circ}\times2\pi\times3\)
Simplify \(\frac{60^\circ}{360^\circ}=\frac{1}{6}\), then:
\(s=\frac{1}{6}\times6\pi\)
\(s = \pi\) yd.

Answer:

\(\pi\) yards