Question

The arc corresponding to a central angle of 125 degrees in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places.

Answer 1

`(Angle)/(360)` x
`2 \pi r`


`(125)/(360)` x
`2 \pi (10)` =
`21.82`

Answer: The Arc measures
`21.82 feet`

Answer 2

`21.82\ ft`

Explanation:

we know that

The circumference of a complete circle is equal to

`C=2\pi r`

In this problem we have

`r=10\ ft`

substitute

`C=2\pi (10)=20 \pi\ ft`

Remember that

An angle of
`360\°` subtends the arc length of a complete circle

so

by proportion

Find the arc length for an angle of
`125\°`

`(20 \pi)/(360)(feet)/(degrees)=(x)/(125)(feet)/(degrees)\\ \\x=125*(20\pi )/360\\ \\x=21.82\ ft`