Question

Can someone please answer. There is one problem. There's a picture. Thank you!

Answer 1

`(165^o)/(360^o)=(11)/(24)\\\\Circumference\ of\ the\ circle:C=2\pi r\\\\r=4\to C=2\pi\cdot4=8\pi\\\\|\widehat{CT}|=(11)/(24)\cdot8\pi=(11)/(3)\pi\approx11.51\\\\Answer:\boxed{11.51}`

Answer 2

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

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

`s = (\pi)/(180)((165)/(4))(4)`

`s = (\pi)/(180)(41.25)(4)`

`s = (\pi)/(180)(165)`

`s = (165\pi)/(180)`

`s = (11\pi)/(12)`

`s = (11\pi)/(12) * (180)/(\pi)`

`s = 11 * 15`

`s = 165\°`

Radians:
`s = \theta r`

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

`s = (165)/(4)(4)`

`s =41.25(4)`

`s =165`

`s =165 * (\pi)/(180)`

`s =11 * (\pi)/(12)`

`s = (11\pi)/(12)`


`Arc\ Length = (central\ angle)/(360) * circumference`

`Arc\ Length = (\theta)/(360) * 2\pi r`

`Arc\ Length = (165)/(360) * 2(3.14)(4)`

`Arc\ Length = (11)/(24) * 2(12.56)`

`Arc\ Length = (11)/(24) * 25.12`

`Arc\ Length = (276.32)/(24)`

`Arc\ Length \approx 11.51\bar{3}`

The answer is A.