The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is \( 31^{\circ} \). If the vertical distance from the bottom to the top of the mountain is 902 feet, what is the length of the gondola ride? Round to the nearest foot. A. 1052 feet B. 465 feet C. 1751 feet D. 773 feet

To find the length of the gondola ride, we can use trigonometry. The angle of elevation (\(31^{\circ}\)) and the vertical height (902 feet) form a right triangle where the opposite side is the vertical distance (902 feet) and the hypotenuse is the length of the gondola ride. We can use the sine function: \[ \sin(31^{\circ}) = \frac{\text{opposite}}{\text{hypotenuse}} \Rightarrow \sin(31^{\circ}) = \frac{902}{L} \] Rearranging gives: \[ L = \frac{902}{\sin(31^{\circ})} \] Calculating that gives us \(L \approx 1751\) feet. So, the answer is C. 1751 feet. If you ever find yourself stuck with steps in problems like this, remember that breaking them down can be helpful. Visualizing the triangle and understanding what each side represents simplifies the whole process. Just don’t forget your calculator or the angle’s sine value! Speaking of scenic rides, did you know the first gondola lift was built in 1936 in Switzerland? It was called the "Gondelbahn" and revolutionized mountain transport, turning hiking into a more accessible activity. So the next time you're zipping up a mountain, remember the history of gondolas and how they’ve made amazing views available to everyone!