Question

If a circular pool has a circular fence around it that has a 20-foot diameter, then what is the measure of the central angle that cuts the arc that measures 4 feet?(1 point)
Responses

22.9 degrees
22.9 degrees

226.2 degrees
226.2 degrees

72 degrees
72 degrees

45.8 degrees
45.8 degrees

Answer 1

To find the measure of the central angle that cuts an arc measuring 4 feet in a circular fence with a diameter of 20 feet, we can use the formula for the arc length \( L \) related to the radius \( r \) and the central angle \( \theta \) in radians.

1. First, we need to find the radius of the circular fence:
\[
\text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{20 \text{ feet}}{2} = 10 \text{ feet}
\]

2. The formula for arc length is:
\[
L = r \theta
\]
where \( \theta \) is in radians.

3. We know the arc length \( L = 4 \text{ feet} \), and we can set up the equation:
\[
4 = 10 \theta
\]

4. Solving for \( \theta \):
\[
\theta = \frac{4}{10} = 0.4 \text{ radians}
\]

5. To convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[
\theta \text{ (degrees)} = 0.4 \times \frac{180}{\pi} \approx 22.9 \text{ degrees}
\]

Thus, the measure of the central angle that cuts the arc that measures 4 feet is approximately **22.9 degrees**.