Pythagorean theorem: sides, word problems and the converse

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Learn it In a right triangle $a^2 + b^2 = c^2$, where c is the hypotenuse (the side opposite the right angle). To find a leg, subtract: $a^2 = c^2 - b^2$.

Example: A 13 m ladder reaches 12 m up a wall. How far is the foot from the wall?

$a^2 = 13^2 - 12^2 = 169 - 144 = 25$.
$a = 5$.
The foot is 5 m from the wall.

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