Question

A building is to be braced by means of a beam which must pass over a wall. If the wall is 3 3/8 feet high and stands 8 feet from the building, find the shortest beam that can be used.

Answer 1

if the beam touches the ground x feet from the wall, and touches the building at a height of y feet, then

x/3.375 = (x+8)/y
y = (27/8)(x+8)/x

The length z of the beam is

z^2 = x^2+y^2 = x^2 + ((27/8)(x+8)/x)^2

Crank through the algebra, and you find that dz/dx=0 at x≈5.9736

So,
y = 7.8949
z = √(13.9736^2 + 7.8949^2) ≈16 feet