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^2a2+b2=c2 , in which aa and bb are the opposite and the adjacent sides, the 2 sides which make the right-angle, and cc representing the hypotenuse, the longest side of the triangle. So if you have a = 6a=6 and b = 8b=8, cc would equal to (6^2 + 8^2)^(1/2)(62+82)12, (x^(1/2)x12 meaning square rooted), which is equal to 10, cc, the hypotenuse.http://ncalculators.com/number-conversion/pythagoras-theorem.htmhttp://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^2a2+b2=c2!

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 aa or which is bb). The cc is always longer than aa and bb! To get some more clarity, take a look at the example down below!
https://autodo.info/pages/p/pythagorean-theorem-problems-hypotenuse/https://autodo.info/pages/p/pythagorean-theorem-problems-hypotenuse/
In this case, lets say that aa is 33, bb is 44 and cc is xx.

a^2+b^2=c^2a2+b2=c2
After substituting...
3^2+4^2=x^232+42=x2
After simplifying...
9+16=x^29+16=x2
Now, solve it!
x^2=25x2=25
Whoa, whoa, wait a second before you finalize that as the answer! We can simplify this. It's just not xx, it's x^2x2! So we have to find the square root of 2525 so that you can get your final answer! The square root of 2525 is 55. So...
x=5x=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.shtmlhttp://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 66 is aa, xx is bb and we know that 1010 has to be cc.

a^2+b^2=c^2a2+b2=c2
After substituting...
6^2+x^2=10^262+x2=102
After simplifying...
36+x^2=10036+x2=100
Leave x^2x2 on one side...
x^2=100-36x2=10036
x^2=64x2=64
x=8x=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!