Question

What is the approximate length of arc s on the circle below? 330 degrees central angle radius 12 feet

Answer 1

`69.08\ ft`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=12\ ft`

substitute

`C=2\pi (12)`

`C=24\pi\ ft`

step 2

Find the approximate length of arc s

we know that

The circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find out the length of arc for a central angle of 330 degrees

`(24\pi)/(360)=(x)/(330)\\\\x=24\pi(330)/360`

`x= 22\pi\ ft` ----> exact value

assume

`\pi =3.14`

`22\pi\ ft=22(3.14)=69.08\ ft` ----> approximate value