What is the Pythagorean Theorem?

The Pythagorean Theorem is a relation in a right-angled triangle. The rule states that `a^2 + b^2 = c^2` , in which `a` and `b` are the opposite and the adjacent sides, the 2 sides which make the right-angle, and `c` representing the hypotenuse, the longest side of the triangle. So if you have `a = 6` and `b = 8`, `c` would equal to `(6^2 + 8^2)^(1/2)`, (`x^(1/2)` meaning square rooted), which is equal to 10, `c`, the hypotenuse.

The Pythagorean Thereom (found by Pythagoras aka Pythagoras of Samos) is used to find the length of a side of a right triangle using the formula `a^2+b^2=c^2`!

A right triangle has two "legs" and a hypotenuse. A hypotenuse is the longest side of a right triangle and is always the opposite of the right angle corner. The legs can be a or b (it doesn't matter which is `a` or which is `b`). The `c` is always longer than `a` and `b`! To get some more clarity, take a look at the example down below!

In this case, lets say that `a` is `3`, `b` is `4` and `c` is `x`.

`a^2+b^2=c^2`
After substituting...
`3^2+4^2=x^2`
After simplifying...
`9+16=x^2`
Now, solve it!
`x^2=25`
Whoa, whoa, wait a second before you finalize that as the answer! We can simplify this. It's just not `x`, it's `x^2`! So we have to find the square root of `25` so that you can get your final answer! The square root of `25` is `5`. So...
`x=5`!

Remember, we don't use the Pythagorean Theorem just for the hypotenuse! We can use it for the other sides, too! Ex:

In this problem, we know the hypotenuse, but we need to find out what one of the "legs" is. Lets say that `6` is `a`, `x` is `b` and we know that `10` has to be `c`.

`a^2+b^2=c^2`
After substituting...
`6^2+x^2=10^2`
After simplifying...
`36+x^2=100`
Leave `x^2` on one side...
`x^2=100-36`
`x^2=64`
`x=8`

There! We have it! I hope you have a better clarity of the Pythagorean Thereom and understand it! My source (despite the images) is my mind! Sorry if my answer is too long!