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 of 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?

We get the distance from the gondola ride to the top of the mountain by noting that this distance is the hypotenuse of the right triangle formed by the side of the mountain and the ground.
                         sin 31° = 902 ft / x
The value of x is equal to 1751.33 ft. 
To determine the amount of time it will take for gondola to travel this distance, we divide the calculated distance by the speed,
                      time = (1751.33 ft) / 155 ft/minute = 11.3 minutes
Thus, the gondola will take about 11.3 minutes.