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.

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 Link

isyllus isyllus · Answer 2 · 2018-12-18T19:54:38+01:00

Answer:

In 14 minutes ride almost last.

Step-by-step 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

[tex]\sin22^{\circ}=\dfrac{689}{\text{Distance covered}}[/tex]

[tex]\text{Distance covered}=689\csc22^{\circ}[/tex]

Speed=130 ft/min

We need to find time to ride last.

[tex]Time=\frac{Distance}{Speed}[/tex]

[tex]Time=\frac{689\csc22^{\circ}}{130}\approx 14\text{min}[/tex]

Thus, In 14 minutes ride almost last.