# Homework Help: Optimization Hallway Problem

1. Nov 13, 2006

### muna580

I have this optimization problem, with the solution, but I don't really understand how to do this. Can someone please explain it to me? I mean, I the solution, I got totally lost when he started working out the problem after that long paragraph. Where did he get the first equation from?

One hallway (which is 4 feet wide) meets another hallway (which is 8 feet wide) in a right-angled corner. What is the length of the longest ladder which can be carried horizontally around the corner? Give an exact answer, assuming the ladder has no width.

2. Nov 13, 2006

### HallsofIvy

I don't understand what more you want. Do you see why $sin(\theta)= \frac{4}{l_1}$? Do you see why $cos(\theta)= \frac{8}{l_2}$? Do you see why $l_1+ l_2= l$?