Question

The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 22°. If the vertical distance from the bottom to the top of the mountain is 689 feet and the gondola moves at a speed of 130 feet per minute, how long does the ride last?

Answer 1

`\sin( \alpha ) = \: (opp)/(hyp)`

`\sin(22) = (689)/(hyp)`

`hyp \: = (689)/( \sin(22) )`

`speed = (distance)/(time)`

`time = ( (689)/( \sin(22) ) )/(130) \: \: \:minutes`

Answer 2

Explanation:

Alright, lets get started.

Please refer the diagram I have attached.

Using SOH CAH TOA in right triangle,

`sin 22=(opposite)/(hypotenuse)`

`sin 22=(689)/(x)`

`x=(689)/(sin 22)`

Plugging the value of sin 22

`x=(689)/(0.3746)`

`x=1839.29` feet

So the distance is 1839.29 feet.

`time=(distance)/(speed)=(1839.29)/(130)`

time=14.15 minutes : Answer

Hope it will help :)