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, what is the length of the gondola ride?

A. 1052 ft
B. 1751 ft
C. 773 ft
D. 465 ft

Answer 1

The length of the gondola ride can be calculated using the sine trigonometric function, and with the angle of elevation at 31 degrees and vertical distance being 902 feet, the gondola ride length comes out to be approximately 1052 feet.

Step-by-step explanation:

The question involves finding the length of the gondola ride given an angle of elevation and the vertical distance to the top of the mountain. Since the gondola path forms a right triangle with the mountain, we can use trigonometric functions to find the length, which is the hypotenuse of the triangle. The angle of elevation is 31 degrees, and the vertical distance (height) is 902 feet. The trigonometric function that relates these two with the hypotenuse (gondola ride length) is the sine function.

Using the sine function, we have:

sin(31°) = ​​height / hypotenuse

sin(31°) = 902 feet / hypotenuse

hypotenuse = 902 feet / sin(31°)

Therefore, the hypotenuse (gondola ride) ​​is approximately ​1052 feet.

So, the answer is A. 1052 ft.