Legs from the Hypotenuse

Now work the other way. You know the hypotenuse of a 45-45-90 triangle and you want the legs. The hypotenuse is the leg times √(2), so the leg is the hypotenuse divided by √(2). When the hypotenuse already has a root of 2 in it, the division is easy. A hypotenuse of 8√(2) means legs of 8.

When the hypotenuse is a plain number, use this fact: dividing by √(2) is the same as multiplying by √(2)/2, because √(2) × √(2) = 2. A hypotenuse of 10 gives legs of 10 × √(2)/2 = 5√(2). You can check the answer with the Pythagorean theorem: (5√(2))^2 + (5√(2))^2 = 50 + 50 = 100 = 10^2. Whichever side you start from, the three sides are always in the ratio 1 : 1 : √2.