Cat Burglar, Crate

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?

Show/Hide Solution

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:

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