# Pythagoras Theorem Calculator

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Lets first understand, what is pythagoras theorem and how we can use pythagoras theorem?

Pythagoras Theorem

The Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. Pythagoras theorem states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

Pythagoras theorem can be written as an equation relating the lengths of the sides a, b and c as a hypotenuse, often called the Pythagorean equation:

$$a^2+b^2=c^2$$Different forms of pythagorean equation

1. \(c=\sqrt{a^2+b^2}\)

2. \(b=\sqrt{c^2-a^2}\)

3. \(a=\sqrt{c^2-b^2}\)

Converse of pythagoras theorem

The converse of the theorem is also true,

For any three positive numbers a, b and c such that \(a^2+b^2=c^2\), there exists a triangle with sides a, b and c, and every such triangle has a right angle between the sides of lengths a and b.

Corollary

1. If \(a^2+b^2=c^2\), then the triangle is right.

2. If \(a^2+b^2>c^2\), then the triangle is acute.

3. If \(a^2+b^2< c^2\), then the triangle is obtuse.

Pythagorean triplets

A Pythagorean triple has three positive integers a, b, and c, such that \(a^2+b^2=c^2.\) Such a triple is commonly written as (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13).

(7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (13, 84, 85), (16, 63, 65), (20, 21, 29), (28, 45, 53), (33, 56, 65)

For calculating the hypotenuse of a triangle using above pythagoras theorem calculator, you have to just write the values in the given input boxes and press the calculate button, you will get the result.