Question

a circle with circumference 48 has an arc with a 30° angle. what is the length of the arc? show your work here

Explanation:

Step1: Calculate the fraction of the circle the arc represents

The total degrees in a circle is \(360^{\circ}\). The arc has a \(30^{\circ}\) angle. The fraction of the circle the arc represents is \(\frac{30}{360}=\frac{1}{12}\)

Step2: Find the arc length

The circumference of the circle is \(C = 48\). The length of the arc \(l\) is the fraction of the circle times the circumference. So \(l=\frac{1}{12}\times48\)

$$l = 4$$

Answer:

4