Question

How long is the ark intersected by a central angle of 5pi/3 radians in a circle with a radius of 2 feet? Round your answer to the nearest 10th. Use 3.14 for pi

Answer 1

10.5 feet

Explanation:

To find the length of the arc intersected by a central angle in a circle, where the central angle is measured in radians, use the arc length formula:

`\large\boxed{\textsf{Arc Length} = r\theta}`

where:

• r is the radius of the circle.
• θ is the central angle measured in radians.

Given values:

• r = 2 feet
• θ = 5π/3 radians
• π = 3.14

Substitute the given values into the arc length formula:

`\begin{aligned}\textsf{Arc Length}&=r\theta\\\\&=2\cdot (5\pi)/(3)\\\\&=2\cdot (5\cdot 3.14)/(3)\\\\&=2\cdot (15.7)/(3)\\\\&=(31.4)/(3)\\\\&=10.466666...\\\\&=10.5\; \sf ft\;(nearest\;tenth)\end{aligned}`

Therefore, the length of the arc is 10.5 feet, rounded to the nearest tenth.