Question

in a circle, the length of an arc intercepted by a central angle is 12 mm, and the radius of the circle is 8 mm. what is the measure, in radians, of the angle? 4 20 1.5 96

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) intercepted by a central angle \(\theta\) (in radians) in a circle of radius \(r\) is \(s = r\theta\).

Step2: Solve for \(\theta\)

We are given that \(s = 12\) mm and \(r=8\) mm. Rearranging the formula \(s = r\theta\) for \(\theta\), we get \(\theta=\frac{s}{r}\).
Substitute \(s = 12\) and \(r = 8\) into the formula: \(\theta=\frac{12}{8}\).
Simplify \(\frac{12}{8}=\frac{3}{2}=1.5\).

Answer:

\(1.5\)