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.
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