Question

The radius of a circle is 20 m.

An arc intercepted by a central angle of the circle is 46 m long.

What is the measure of the central angle, in radians?

Enter your answer in the box. Round your answer to the nearest tenth if necessary.

Answer 1

To find the measure of the central angle in radians, we can use the formula for arc length:

\[
L = r \theta
\]

where \( L \) is the arc length, \( r \) is the radius, and \( \theta \) is the central angle in radians.

We have:
- \( L = 46 \) m (length of the arc)
- \( r = 20 \) m (radius of the circle)

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

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

Substituting the known values:

\[
\theta = \frac{46}{20}
\]

Calculating the fraction:

\[
\theta = 2.3 \text{ radians}
\]

Thus, the measure of the central angle is:

\[
\boxed{2.3}
\]