The Pythagoras theorem is one of the earliest theorems among the ancient civilisation. The theorem is given as “In a right angled triangle the square of the hypotenuse is equal to the sum of the square of the other two sides’’. It is named after the Greek mathematician and philosopher Pythagoras as he is the one who provided a proof of this theorem.

The theorem is mathematically represented as :

[latex]a^{2}+b^{2}=c^{2}[/latex]

Where c is the hypotenuse of the given triangle and a & b are the other two sides of the triangle.

**Note-** Pythagoras Theorem is only applicable to Right-angled Triangle.

Real life uses of the Pythagorean Theorem:

**Navigation-**Pythagoras Theorem has it’s real life application in two- dimensional navigation, by which we can find the shortest distance. For example: If you are navigating from one point to any other point, which is 600 miles towards north and 700 miles towards west, you can use the theorem to find out the distance of one point from another point and can calculate how many degrees you have to travel towards west of north to reach the destination point. Here the distance towards north and west are the two sides of the triangle and the shortest path connecting these two sides is diagonal. This principle can be used for navigation.**Construction:**In Pythagoras theorem, the two sides are used to calculate the length of the diagonal connecting them. This application is used in architecture, Physical constructions, wood working, etc. For example: If you are asked to build a building having a slope, then if the height of the roof and the length it has to cover is known then you can use Pythagoras theorem to calculate the diagonal length of the roof’s slope.**Survey-**This process is mostly used by the cartographers, in order to determine the height and distance between different points for the creation of maps. Pythagoras theorem is also used to calculate the slope of the hills and steepness of the mountains.**Square Angles-**To make sure buildings are square, Pythagoras theorem is used. For the construction of a foundation or laying out a square between two walls, construction workers have to set out a 3-foot by 4-foot by 5-foot triangle, that will always be a right angled triangle. If the lengths are measured correctly, then the corner opposite to that of the triangle’s hypotenuse corresponds to the right angle, so the workers will know that they are building the wall on the right lines.

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**About author:**

Supriya Pandey is an Engineer and an education counsellor by profession. She is presently working with Byju’s as a content writer.

**Mail- supriya.pandey@byjus.com**