Answer:
20.94 ft
Step-by-step explanation:
To find the length of an arc in a circle, you can use the formula:
\[ \text{Arc Length} = \frac{\text{angle}}{360^\circ} \times 2\pi r \]
Where:
- \( \text{Arc Length} \) is the length of the arc.
- \( \text{angle} \) is the central angle in degrees.
- \( r \) is the radius of the circle.
Given:
- Radius \( r = 10 \) ft.
- Angle \( \text{angle} = 120^\circ \).
Substitute the values into the formula:
\[ \text{Arc Length} = \frac{120}{360} \times 2\pi \times 10 \]
\[ \text{Arc Length} = \frac{1}{3} \times 20\pi \]
\[ \text{Arc Length} = \frac{20\pi}{3} \]
\[ \text{Arc Length} \approx \frac{20 \times 3.14159}{3} \]
\[ \text{Arc Length} \approx \frac{62.8318}{3} \]
\[ \text{Arc Length} \approx 20.9439 \text{ ft} \]
So, the length of the arc is approximately 20.94 feet.
