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.

Question

Mathematics

Gretchen Carroll

4 February, 02:19

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.

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Karina Acevedo · 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)