Question

If the arc of a circle is 15 meters long and the radius of the circle is 3 meters, then what is the measure of the central angle, to the nearest tenth of a degree, that intercepts that 15-meter arc?(1 point)
Responses

7.9 degrees
7.9 degrees

353.4 degrees
353.4 degrees

286.5 degrees
286.5 degrees

282.7 degrees

Answer 1

To find the measure of the central angle that intercepts an arc of a circle, we can use the formula:

\[
\text{Arc Length} = r \times \theta
\]

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

From the problem, we know:
- Arc Length = 15 meters
- Radius = 3 meters

We can substitute these values into the formula:

\[
15 = 3 \times \theta
\]

Next, solve for \( \theta \):

\[
\theta = \frac{15}{3} = 5 \text{ radians}
\]

Now, to convert radians to degrees, we use the conversion factor \(\frac{180^\circ}{\pi}\):

\[
\theta \text{ (in degrees)} = 5 \times \frac{180^\circ}{\pi}
\]

Calculating this gives:

\[
\theta \approx 5 \times 57.2958 \approx 286.5^\circ
\]

So, the measure of the central angle, to the nearest tenth of a degree, is:

**286.5 degrees**.