Question

find the measure of \\( \theta \\), in radians, if \\( r = 7 \\) and the arc length is 10.5. \\( \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 can rewrite the formula as \(\theta=\frac{s}{r}\). Given \(s = 10.5\) and \(r = 7\), substitute these values into the formula: \(\theta=\frac{10.5}{7}\).

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

\(\frac{10.5}{7}=1.5\)

Answer:

\(1.5\) radians