A 125-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 25 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.

Answer 1

Consider a right triangle formed by the horizontal distance H, the vertical distance V, and the diagonal brace, L=125'.

Since
H=V+25
apply Pythagoras theorem:
H²+V²=L²
(V+25)²+V²=125²
Expand and simplify:
2V²+50V+625 = 15625
or
2V²+50V-15000=0

Solve for V by factoring or quadratic formula. Reject negative value for x.

Post your answer for checking, or back-substitute to check.