Question

What is the measure of the central angle of a circle with radius 24 ft that intercepts a 10 ft arc? Use 3.14 for π . Round the answer to the hundredths place. Enter your answer in the box.

Answer 1

23.89 degrees

Explanation:

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Answer 2

Answer: 23.89 degrees

The full circle has the circumference as follows:

`2\pi r = 2\pi\cdot 24\mbox{ft}=150.72\mbox{ft}`

The ratio of 10 ft to the full 150.72 ft is the same as the ratio of the angle x to the full angle 2pi (or 360 degrees):

`(10)/(150.72)=(x)/(2\pi)\\x = 2\pi\cdot(10)/(150.72) = 360 ^\circ\cdot(10)/(150.72)=23.89^\circ`