Question

find the measure of θ, in radians,
if r = 5 and the arc length is 15.5.
θ = ? 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 can rewrite the formula \(s = r\theta\) to solve for \(\theta\) as \(\theta=\frac{s}{r}\).
Given \(s = 15.5\) and \(r = 5\), substitute these values into the formula: \(\theta=\frac{15.5}{5}\).

Step3: Calculate the value of \(\theta\)

\(\theta=\frac{15.5}{5}=3.1\)

Answer:

\(3.1\)