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?
20
1.5
96
4

Answer 1

To find the measure of the central angle in radians when given the length of the arc and the radius of the circle, you can use the formula for the length of an arc:

\[
L = r \theta
\]

where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.

Given that:
- \( L = 12 \) mm,
- \( r = 8 \) mm,

we can rearrange the formula to solve for \( \theta \):

\[
\theta = \frac{L}{r}
\]

Now, substituting in the values we have:

\[
\theta = \frac{12 \, \text{mm}}{8 \, \text{mm}} = \frac{12}{8} = 1.5 \text{ radians}
\]

Thus, the measure of the angle in radians is \( \boxed{1.5} \).