Optimization Problems -____-

[Aqua]

A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. 
What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

I know it involves similar triangles... BUT I DON'T GET IT ;____;

[Lore]

Check either this quiz: http://www.math.umn.edu/~rusin018/1271_Fall_2006/1271_quiz_7_sol.pdf
First question.

Or, here's an answer I found online:
"That would be 12 feet times the square root of 2, (or1.414...) assuming the ladder is straight and rigid. If it's a rope ladder then the answer is 12 feet. Actually, I have had some more time to think about this and I now believe my first answer was incorrect. The ladder length equals 8sec(theta)+4sec(ninety-theta) ........where theta is the angle of the ladder against the wall of the building. I believe the correct answer is for an angle theta of 30 degrees. To find the correct answer mathematically, you would need to take the first derivative of this equation and find the angle theta where the first derivative is zero, since this will be the point in the curve where the ladder is the smalIest or at a minimum. I hope this helps."

[fugibo]

relative minima + inverse of a function
I'm too lazy to do it myself, but it sounds pretty easy.