It is night. You are in a quiet city, near the sea. There is no moon. Near a wharf, a cubical wooden shipping crate is lying along the outside wall of a warehouse, flat against the wall. Each edge of the crate is 1 meter. At midnight, out of the crate emerges Cathy, the notorious cat burglar. She noiselessly leans a √15 meter ladder against the wall in such a way that it just grazes the free horizontal edge of the crate. At what height does the ladder hit the wall?

To make the computation feasible, we’ll assume there could be a ladder whose length might be described as √15 meters. We use the Pythagorean Theorem and similar triangles to get: