Pythagorean theorem: find a leg, step by step
Finding a leg runs the theorem backward: the hypotenuse squared minus the known leg squared, then a square root.
The question
cm
Right triangle, 34 and 16
- The hypotenuse is the side OPPOSITE the right angle — never one of the two that make the corner. It is also always the longest, so you can check yourself twice.
- Here the hypotenuse is given — 34 cm — and a LEG is missing. That is the case where the sum is a subtraction, not an addition.
- Square the two you have: 34² = 1156 and 16² = 256.
- The leg's square is what is LEFT when you take the other leg's square off the hypotenuse's: 1156 − 256 = 900.
- That is the square, not the side. Take the square root: √900 = 30 cm.
How it works.
- 01
The hypotenuse is the side OPPOSITE the right angle — never one of the two that make the corner. It is also always the longest, so you can check yourself twice.
- 02
Here the hypotenuse is given — 34 cm — and a LEG is missing. That is the case where the sum is a subtraction, not an addition.
- 03
Square the two you have: 34² = 1156 and 16² = 256.
- 04
The leg's square is what is LEFT when you take the other leg's square off the hypotenuse's: 1156 − 256 = 900.
- 05
That is the square, not the side. Take the square root: √900 = 30 cm.