Legs from the Hypotenuse

Going the other way, a leg is the hypotenuse divided by √2. Dividing by a root is awkward, so it is usually written with the root on top: multiply top and bottom by √2.

$\frac{10}{\sqrt{2}} = \frac{10\cdot \sqrt{2}}{2} = 5\cdot \sqrt{2}$

So a 45-45-90 triangle with hypotenuse 10 has legs of $5\cdot \sqrt{2}$. A quick way to see it: the leg is half the hypotenuse times √2. Check with Pythagoras: two legs squared are 50 + 50 = 100 = 10².