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

We represent the prob. by a rt triangle:

h = height = ver side.
(h + 25) = hor. side.
hyp. = 125 ft.

(h + 25)^2 + h^2 = (125)^2,
h^2 + 50h + 625 + h^2 = 15625,
2h^2 + 50h - 15000 = 0
Divide both sides by 2:
h^2 + 25h - 7500 = 0,
(h - 75)(h + 100) = 0,

h - 75 = 0,
h = 75 Ft. = ver. dist.

h + 25 = 75 + 25 = 100 Ft. = hor. dist.

X + 100 = 0,
X = -100.

Use positive value of X:
X = 75 FT.

X + 25 = 75 + 25 = 100 Ft. =

Answer 2

horizontal distance =100 Ft
vertical distance=75 ft