Question

A merry-go-round has a radius of 18 feet. If a passenger gets on a

horse located at the edge of the wheel and travels 38 feet, find the
angle of rotation to the nearest degree.

Answer 1

Answer and Step-by-step explanation:

`Greetings!`

`Let's~answer~ your ~question!`

`\underline{\bold{It~is~given~that:}}`

`The ~radius~ of ~the ~round ~path: r = 18~ feet`

`The~ length ~of ~the ~distance ~cover ~by ~wheel : l = 38 ~feet`

`Let ~The ~angle~ of ~rotation :\phi`

`\underline{\bold{Now, ~According ~to~ question:}}`

`\therefore length~ of ~the ~arc~ of ~a ~circle ~subtending ~an ~angle~ at~ center = \phi`

`length ~of ~the ~distance ~cover ~by ~wheel =\boxed{~~ \pi * radius *~(\phi)/(180\degree^(o) )~ ~}`

`Since ~180^(o) \ = \pi ~radian`

`So,~ length~ of~ the ~distance~ cover~ by ~wheel~ \boxed{~~180^(o) * raius * (\phi)/(180^(o)) ~~}`

`\underline{\bold{i.e:}}`

`l=r * \phi`

`Or, \phi=(38~feet)/(18~feet)`

`Or,~\phi =2.11^(o)`

`\bold{Thus,~the~angle~of~rotation~is=2.11^(o)}`

Answer 2

121 degrees

Explanation:

The "arc length" formula is s = rФ, where Ф represents the central angle in radians (not degrees).

Here r = 18 ft and s = 38 ft, and so:

38 ft

s = rФ becomes Ф = ------------ = 2.111 radians

18 ft

which, in degrees, is:

2.111 rad 180 deg

------------- * --------------- = 121 degrees, to the nearest degree

1 3.142