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? Round to the nearest minute.

Answer 1

You would need to divide the length of the hypotenuse by the velocity of the ride.

sinα=height/hypotenuse

hypotenuse=height/sinα

time=hypotenuse/velocity of ride.

time=height/(velocity * sinα)

We are given that height=689ft, velocity=130ft/min, and α=22° so

t=689/(130sin22)

t≈14 min (to nearest whole minute)

Answer 2

In 14 minutes ride almost last.

Explanation:

The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 22°

f 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.

Please see the attachment for the figure.

Using trigonometry identity

`\sin22^(\circ)=\frac{689}{\text{Distance covered}}`

`\text{Distance covered}=689\csc22^(\circ)`

Speed=130 ft/min

We need to find time to ride last.

`Time=(Distance)/(Speed)`

`Time=(689\csc22^(\circ))/(130)\approx 14\text{min}`

Thus, In 14 minutes ride almost last.