The sum of the areas of the two squares on the legs ($a$ and $b$) equals the area of the square on the hypotenuse $c$.
We can imagine something like this:
The right Triangle whose length of sides is equal to $3, 4$ and $5$ is called the Egyptian triangle.
Let’s forget that we know that the length of hypotenuse is equal to $5$ and try to calculate it using Pythagorean theorem.
In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
And it is valid in different order:
If the square of the hypotenuse is equal to the sum of the squares of the other two sides the triangle is a right angled.
$\ c^2 = a^2 + b^2$
Where $ a = 4$, and $ b = 3$.
$ c^2 = 4^2 + 3^2$
$ c^2 = 16 + 9$
$ c^2 = 25$
If we know lengths of any two sides of a right triangle, we can use this theorem to quickly find the third.
$ c^2 = a^2 + b^2$
Where $ c = 10$, and $ b = 83$.
$ a^2 = c^2 – b^2$
$ a^2 = 100 – 64$
$ a^2 = 36$
$ a = 6$
If we have any other triangle, we can also use Pythagorean theorem.
If we have length of $b$ and $v_a$, and $a=12$ we can find out other lengths in these triangle:
Now, we can calculate:
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