To determine the arc length intersected by a central angle of [tex]\(\frac{5 \pi}{3}\)[/tex] radians in a circle with a radius of 2 feet, we follow these steps:
1. Convert the angle in radians to a numerical value using [tex]\(\pi \approx 3.14\)[/tex]:
[tex]\[
\frac{5 \pi}{3} \approx \frac{5 \times 3.14}{3}
\][/tex]
2. Calculate the numerical value of the angle:
[tex]\[
\frac{5 \times 3.14}{3} = \frac{15.7}{3} = 5.233333333333333
\][/tex]
3. Use the formula for the arc length:
[tex]\[
\text{Arc length} = \text{Angle in radians} \times \text{Radius}
\][/tex]
4. Substitute the angle in radians and radius into the formula:
[tex]\[
\text{Arc length} = 5.233333333333333 \times 2 = 10.466666666666667
\][/tex]
5. Round the result to the nearest tenth:
[tex]\[
10.466666666666667 \approx 10.5
\][/tex]
Therefore, the length of the arc intersected by a central angle of [tex]\(\frac{5 \pi}{3}\)[/tex] radians in a circle with a radius of 2 feet, rounded to the nearest tenth, is [tex]\(10.5\)[/tex] feet.
The correct answer is:
10.5 ft.
