Question

A deep mountain valley is separated by two vertical cliffs. One cliff is 600 meters high and the other is 400 meters high. A cable car runs from the foot of each cliff to the top of the other cliff. At what height above the ground do the two cable cars cross? Be sure to draw a diagram.

Answer 1

Let L be the distance between cliffs and y be the height where the cables intersect, x is the horizontal distance from the lower cliff to below the intersection point.

y/x = 600/L
y/(L-x) = 400/L
(L-x)/y * (y/x) = 600/400 = 3/2
(L-x)/x = 3/2
L/x -1 = 3/2
L/x = 5/2
x/L = 2/5
y = (x/L)*600 = 240 m

You will have to draw your own figure.