Railroad problem. Dealing with angles

Question

The steepest Railway in the world is Katoomba Scenic Railway in Australia. The passenger car is pulled up the mountain by twin steel cables. It travels along the track 1020 feet to obtain a change in altidude of 647 feet. 

a.)Find the angle of elevation in the railway

b.)How far does the car travel in a horizontal direction

Answer 1

Imagine that the train is traveling along the hypotenuse of a right triangle. The angle of elevation is the angle opposite the side of the triangle representing elevation gain.

 

To calculate the angle, use the sine function

 

Sine θ = opposite side length / hypotenuse length

where θ is the angle of elevation in degrees

 

sine θ = 647 / 1020 = 0.6343

θ = angle of elevation = 39.4 degrees

 

To find the horizontal distance traveled, use the cosine function for the angle of elevation

 

Assume horizontal distance  = x

 

cos θ = adjacent side length/ hypotenuse length

 

cos (39.4) = x/1020

 

x = (1020) (0.773)

x = horizontal distance traveled = 788.2 feet