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 96 20 1.5

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians.

Step2: Solve for the angle $\theta$

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: $\theta=\frac{12}{8}=\frac{3}{2}=1.5$ radians.

Answer:

1.5