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 1.5 20

Explanation:

Step1: Recall arc length formula

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

Step2: Solve for \( \theta \)

We know \( s = 12 \) mm and \( r = 8 \) mm. Rearranging the formula \( s = r\theta \) to solve for \( \theta \), we get \( \theta=\frac{s}{r} \). Substituting the given values, \( \theta = \frac{12}{8} \).

Step3: Simplify the fraction

Simplifying \( \frac{12}{8} \) gives \( \frac{3}{2}=1.5 \).

Answer:

1.5 (corresponding to the option "1.5")