Welcome to Business Analytics blog :): The Pythagorean Theorem

Lets learn to calculate the distance. There are various technique available for doing this, but one of the most popular technique is Pythagorean theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras's theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation":^[1]
$a^2 + b^2 = c^2\!\, ,$

where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

Definition
The longest side of the triangle is called the "hypotenuse", so the formal definition is:

In a right angled triangle:
the square of the hypotenuse is equal to
the sum of the squares of the other two sides.

Why Is This Useful?

If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)

How Do I Use it?

Write it down as an equation:

a² + b² = c²

Pythagorean proof

The Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it. In any event, the proof attributed to him is very simple, and is called a proof by rearrangement

Other forms of the theorem

As pointed out in the introduction, if c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation:

$a^2 + b^2 = c^2 .\,$

If the length of both a and b are known, then c can be calculated as

$c = \sqrt{a^2 + b^2}. \,$

If the length of the hypotenuse c and of one side (a or b) are known, then the length of the other side can be calculated as

$a = \sqrt{c^2 - b^2} \,$

or

$b = \sqrt{c^2 - a^2}. \,$

The Pythagorean equation relates the sides of a right triangle in a simple way, so that if the lengths of any two sides are known the length of the third side can be found. Another corollary of the theorem is that in any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum.
Example: Does this triangle have a Right Angle?
Does a² + b² = c² ?

a² + b² = 10² + 24² = 100 + 576 = 676

c² = 26² = 676

They are equal, so ...

Yes, it does have a Right Angle!
Regards

Saurabh