Question

a circle with circumference 186 has an arc with a 60° angle. what is the length of the arc?

Explanation:

Step1: Find the fraction of the circle the arc represents

The total degrees in a circle is \(360^{\circ}\). The arc has a \(60^{\circ}\) angle. The fraction of the circle the arc represents is \(\frac{60}{360}=\frac{1}{6}\).

Step2: Calculate the arc length

The circumference of the circle is \(C = 186\). The length of the arc \(s\) is the fraction of the circle times the circumference. So \(s=\frac{1}{6}\times186\).

$$s=\frac{186}{6}=31$$

Answer:

31