What is the Pythagorean Theorem?

2 Answers
Nov 24, 2014

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.http://ncalculators.com/number-conversion/pythagoras-theorem.htm

Aug 24, 2017

Trust me, it's a very helpful topic in Geometry and you can learn more about it down below!

Explanation:

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!
https://autodo.info/pages/p/pythagorean-theorem-problems-hypotenuse/
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: http://www.myghillie.info/lsitpkey-pythagorean-theorem-formula-cute.shtml

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!