Question

Find the length of an arc of 40° in a circle with an 8 inch radius

Answer 1

Radians:
`s = \theta r`

`s = (s)/(r)(r)`

`s = (40)/(8)(8)`

`s = 5(8)`

`s = 40\°`

`s = (4\pi)/(18)`

Degrees:
`s = \theta(\pi)/(180)r`

`s = (s\pi)/(180r)(r)`

`s = (40\pi)/(180(8))(8)`

`s = (40\pi)/(180)`

`s = (4\pi)/(18)`

`s = 40\°`

Arc Length =
`(\theta)/(360\°) * C`
Arc Length =
`(5\°)/(360\°) * 2\pi r`
Arc Length =
`(1)/(72) * 2(3.14)(8)`
Arc Length =
`(1)/(72) * 2(25.12)`
Arc Length =
`(1)/(72)(50.24)`
Arc Length ≈
`0.698131701`