Question

The High Roller wheel in Las Vegas has a diameter of 520 feet and its base is 30 feet off the ground. You board a gondola on the wheel and rotate 240 degrees counterclockwise before the wheel temporarily stops. How high above the ground are you when the wheel stops?

Answer 1

420 feet

Explanation:

GIVEN: The High Roller wheel in Las Vegas has a diameter of
`520` feet and its base is
`30` feet off the ground. You board a gondola on the wheel and rotate
`240` degrees counterclockwise before the wheel temporarily stops.

TO FIND: How high above the ground are you when the wheel stops?

SOLUTION:

Consider the figure attached.

As wheel rotate counter clockwise
`240^(\circ)`, its current position is
`120^(\circ)` clock wise.

Total height
`=260+30+h\rightarrow290+h`

Calculating value of
`h`

`\sin 30^(\circ)=(h)/(260)\impliesh=260\sin30^(\circ)`

`\implies h=260*(1)/(2)=130feet`

Total height
`=290+130` feet

`=420\text{ feet}`

Hence total height is 420 feet