To find the measure of the central angle that intercepts a given arc length, you can use the formula:
\[ \text{Arc Length} = r \cdot \theta \]
Where:
- \( \text{Arc Length} \) is the length of the arc,
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.
First, rearrange the formula to solve for \( \theta \):
\[ \theta = \frac{\text{Arc Length}}{r} \]
Plugging in the given values:
\[ \text{Arc Length} = 15 , \text{meters} \] \[ r = 3 , \text{meters} \]
\[ \theta = \frac{15}{3} = 5 \text{ radians} \]
Now, to convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \):
\[ \theta = 5 \times \frac{180}{\pi} \approx 5 \times 57.2958 \approx 286.5 \text{ degrees} \]
Thus, the measure of the central angle that intercepts the 15-meter arc is approximately 286.5 degrees.
The answer is:
286.5 degrees.