Question

Find the length of the arc shown in brown. Leave your answer in terms of pi.

Answer 1

The length of the arc is
`8\pi\ ft`

Explanation:

we know that

The measure of the arc shown in brown is equal to

`180\°-60\°=120\°` -----> by central angle

Remember that

The length of the arc of the complete circle (360 degrees) is equal to the circumference

`C=\pi D`

we have

`D=24\ ft`

substitute

`C=\pi (24)=24 \pi\ ft`

so

by proportion

Find the length of the arc for a measure of
`120\°`

`(24\pi )/(360) (ft)/(degrees) =(x )/(120) (ft)/(degrees)\\ \\x=120*(24\pi )/360\\ \\ x= 8\pi\ ft`