Pythagors' theorum allows one to calculate the lenght of the "opposite" side (That is, opposite to the right angle) in a right-angled triangle By knowing only the lengths of the other two sides. It can also be mixed with the sine and cosine rules, trigonometry and such to calculate every angle and side length in pretty much any structure. Practical uses involve the measurement of buildings and such.
•Use the same unit of measurement for all sides.
•Sqaure the lengths of the two shorter sides
•Add the sqaures of the numbers toghether
•Find the sqaure root of that number
•Your answer is the length of the longest side.
Side A is 5cm, side B is 4cm and side C is unknown.
A- 5x5= 25 square cm
B- 4x4= 16 square cm
Square root of 36= 6.
Side C is 6cm.
Of course, this can also be worked backwards to find the length of the smaller sides, provided there are at least two sides given.
If you try to practically apply this with any lengths other than those given, you will end up with decimals. The above example is the only one that does not end in decimal places.