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For a mnemonic recalling the Greek mathematician's formula governing the lengths of each side of a right-angled triangle:

This mnemonic is the punchline of a very old joke, but its serves its purpose extremely well! If you've never heard the joke before, there were 3 Indians who met to trade wives, and the first Indian told his wife to sit on a blanket made from the skin of a deer, while the second Indian placed his wife on a hide made of buffalo... (etc)!

The hypotenuse is the term for the side opposite the 90° right-angle. The theorem enables one to find the length of any side given the lengths of the other two sides, eg. height=²/(hypotenuse²-base²). Other right-angle triangle solutions are obtained by using sine, cosine and tangent ratios.