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

72 degrees
72 degrees

45.8 degrees
45.8 degrees

226.2 degrees

Answer 1

To find the measure of the central angle that cuts an arc of a circular fence with a diameter of 20 feet and an arc length of 4 feet, we can use the formula for the arc length:

\[
L = r \cdot \theta
\]

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

First, we need to calculate the radius \( r \) of the circular fence, which is half of the diameter:

\[
r = \frac{20 \text{ feet}}{2} = 10 \text{ feet}
\]

Next, we can rearrange the formula to solve for \( \theta \):

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

Substituting the values we have:

\[
\theta = \frac{4 \text{ feet}}{10 \text{ feet}} = 0.4 \text{ radians}
\]

To convert radians to degrees, we multiply by \(\frac{180}{\pi}\):

\[
\theta_{\text{degrees}} = 0.4 \cdot \frac{180}{\pi} \approx 22.918 \text{ degrees} \approx 22.9 \text{ degrees}
\]

Thus, the measure of the central angle that cuts the arc that measures 4 feet is approximately:

**22.9 degrees**