Question

a circle with circumference 540 has an arc with a 10° angle. what is the length of the arc?

Explanation:

Step1: Calculate the proportion of the arc

The proportion of the arc with a \(10^{\circ}\) angle in a full - circle (\(360^{\circ}\)) is \(\frac{10}{360}=\frac{1}{36}\).

Step2: Calculate the arc length

Since the circumference of the circle is \(C = 540\), and the arc length \(l\) is a proportion of the circumference. Using the formula \(l=\frac{\theta}{360}\times C\) (where \(\theta\) is the central angle of the arc in degrees and \(C\) is the circumference of the circle), we substitute \(\theta = 10\) and \(C = 540\).
\(l=\frac{10}{360}\times540\)
First, simplify \(\frac{10}{360}=\frac{1}{36}\), then \(l=\frac{1}{36}\times540\)
\(l = 15\)

Answer:

15