Question

the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 31 degrees. if the vertical distance from the bottom to the top of the mountain is 902 feet and the gondola moves at a speed of 155 feet per minute, how long does the ride last? round to the nearest minute

Answer 1

Answer:

The ride lasts 10 minutes.

Step-by-step explanation:

The triangle that is formed is attached.

In order to find out how long the ride lasts, we need to figure out the horizontal distance $d.$

From trigonometry we have:

$tan(31^o)=\frac{902}{d}.$

Therefore

$d=\frac{902\:feet}{tan(31^o)}=1501\:feet.$

Now the amount of time $t$ the gondola ride lasts is equal to the distance $d$ divided by the speed of the gondola:

$t=\frac{1501ft}{155ft/sec} =\boxed{9.69\:minutes.}$

To the nearest minute this is 10 minutes.