What is the Pythagorean Theorem?

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What is the Pythagorean Theorem?

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Answer 1 · 2014-11-24T22:47:07

The Pythagorean Theorem is a relation in a right-angled triangle. The rule states that $a^{2} + b^{2} = c^{2}$ $a^2 + b^2 = c^2$ , in which $a$ $a$ and $b$ $b$ are the opposite and the adjacent sides, the 2 sides which make the right-angle, and $c$ $c$ representing the hypotenuse, the longest side of the triangle. So if you have $a = 6$ $a = 6$ and $b = 8$ $b = 8$ , $c$ $c$ would equal to ${(6^{2} + 8^{2})}^{\frac{1}{2}}$ $(6^2 + 8^2)^(1/2)$ , ( $x^{\frac{1}{2}}$ $x^(1/2)$ meaning square rooted), which is equal to 10, $c$ $c$ , the hypotenuse.http://ncalculators.com/number-conversion/pythagoras-theorem.htm

Answer 2 · 2017-08-24T01:36:33

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 $a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$ !

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 $a$ $a$ or which is $b$ $b$ ). The $c$ $c$ is always longer than $a$ $a$ and $b$ $b$ ! 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 $a$ $a$ is $3$ $3$ , $b$ $b$ is $4$ $4$ and $c$ $c$ is $x$ $x$ .

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

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 $6$ $6$ is $a$ $a$ , $x$ $x$ is $b$ $b$ and we know that $10$ $10$ has to be $c$ $c$ .

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

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!

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What is the Pythagorean Theorem?

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