Question

find the measure of \\( \theta \\), in radians, if \\( r = 5 \\) and the arc length is 15.5. \\( \theta = \\) ? radians

Explanation:

Step1: Recall the arc - length formula

The formula for arc length is \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians.

Step2: Solve for \(\theta\)

We need to isolate \(\theta\). From \(s = r\theta\), we can get \(\theta=\frac{s}{r}\).
Given \(s = 15.5\) and \(r = 5\), then \(\theta=\frac{15.5}{5}\).
\(\theta = 3.1\)

Answer:

\(3.1\)