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 0.6 20 1.5

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 with radius \( r \) is \( s = r\theta \).

Step2: Solve for the central angle \( \theta \)

We are given that \( s = 12 \) 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, we have \( \theta = \frac{12}{8} \).
Simplifying \( \frac{12}{8} \), we divide both the numerator and the denominator by 4, which gives \( \frac{3}{2}=1.5 \).

Answer:

1.5