Question

A 150-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 30 ft longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.

Answer 1

draw a diagram and let the vertical height = x



use pythagoras' theorem to form a quadratic equation

150^2 = x^2 + (x + 30)^2

or

2x^2 + 60x -21600 = 0

or

x^2 + 30x - 10800 = 0

this quadratic factorises so use the positive solution for x as measurement can only be positive

the quadratic