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 are given \(s = 10.5\) and \(r=7\). Rearranging the formula \(s = r\theta\) for \(\theta\), we get \(\theta=\frac{s}{r}\).
Substitute \(s = 10.5\) and \(r = 7\) into the formula: \(\theta=\frac{10.5}{7}\).

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

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

Answer:

\(1.5\) radians