Real Life Uses Pythagorean Theorem

Pythagorean Theorem is named after a Greek philosopher and mathematician Pythagoras. It is used as a base for various mathematical problems. You must have heard about the theorem in your Math class every now and then. But many fail to realize that this theorem finds application in various real life situations.

Pythagorean Theorem

According to Pythagoras Theorem the sum of squares of two sides of a right angled triangle is equal to the square of the hypotenuse. Let one side of triangle be a, the other side be b and hypotenuse is given by c. Now, according to Pythagoras theorem the mathematical formula is represented by [latex]a^{ 2 } + b^{ 2 } = c^{ 2 }[/latex]

Pythagorean Theorem

Some real life applications of Pythagoras theorem are discussed below:

 Square Angles In Buildings

To make sure that the buildings are in square shape, Pythagorean Theorem is used. A set of Pythagorean triplets are used to construct square corners between two walls for example a 5 foot by 12 foot by 13 foot triangle will always be a right angled triangle. The workers will set out a triangle with these lengths to construct a square corner between the two walls. A builder will know whether they are working on a right track if the proper lengths of the strings are used during construction of the right angled triangle.

Surveying In Topographical Sheets 

This theorem finds huge application in the field of geography for the construction of various topographical sheets. In the process of surveying, cartographers are able to calculate the numerical distances and heights between points while creating a map. During the calculation of the steepness of slope of a hill or a mountain, Pythagoras Theorem is used. Surveyor looks through the telescope towards the measuring stick which is at a fixed distance; so that the telescope’s line of sight and the measuring stick form a right angle.

Architecture and Construction 

If you are given a set of straight lines then Pythagoras Theorem can be used to calculate the diagonal connecting them. This finds application in various architectural fields, mechanical labs, during the construction of roofs, etc.

Painting on a Wall 

The painter needs to determine how tall a ladder should be, as it will help to safely determine the distance at which the base needs to be placed away from the wall so that it won’t tip over.


In case of two-dimensional navigation, Pythagoras Theorem can be used to calculate the shortest distance between 2 points. For example, if you are in the middle of a desert and you want to navigate to a point which is 200 kilometers south and 300 kilometers east, you can use the theorem to find out how many degrees east of south you need to travel to reach your desired point. The east and south will be the two legs of the triangle and the shortest line connecting them will be the diagonal. Air navigation can also use this principle to find out the proper place to begin the descent of plane, to land to a particular airport.

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 About the author:

AkshayAgnihotri is an Engineer and a tech enthusiast. He loves writing and blogging along with part-time teaching. He is presently exploring all about the digital education with Byju’s-the Learning App.