Applications Of Pythagoras Theorem In Daily Life

Pythagorean Theorem Introduction: Pythagorean Theorem  is invented by a Greek mathematician named Pythagoras from southern-Italy. He is the first mathematician to use his theorem to understand the real time application in day to day life. The theorem gives the relation between three triangle in Euclidean Geometry, which gives the formula to find length of the sides of any right triangle.

Maths Pythagorean Theorem: In any triangle the square on its largest side is equal to the sum of the squares on the reaming two sides. The triangle is right angled triangle and the angle opp to the largest side of the given triangle is called as hypotenuse of the triangle. The equation of  Pythagorean Theorem is given as a2 = b+ c2  which relates the length of the sides of the given three triangles.


Three Combined Triangles

Fig a: Three combined triangles

Applications of Pythagoras theorem: Application of Pythagorean theorem  are used in daily life like  to determine the slope of the triangle, in buildings. trajectory of a bullet,building fences,Navigation, GPS,Oscilloscopes,Mechanical Engineering calculation,Design engineering,Architecture Polar coordinates,Trigonometry, used in math for oceanography and Calculus. The application of the right angled triangle, especially the 3-4-5 triangle have been proved from vast years in the subject of mathematics.The Pythagorean Theorem can be used with any shape and for any formula that squares a number.  The Pythagorean Theorem only applies to right triangles. Since this triangle has a right angle, the sum of the squares of the other two sides can be used to find r.


Proof of Applications of Pythagoras theorem are given below

1.  To find the distance between the two given points:
     A car travels 20 km from west to east. Then it turns left and travels a further 15 km. Find the displacement between the starting        point and the destination point of the car

Pythagorean Theorem

Fig b : Direction of the Car

 Solution by using  Pythagorean Theorem.
              AC2 = AB2 + BC2
              AC2 = 202 + 152
              AC2 = 625
              AC = 25


2. Determine whether given triangle is a right triangle.

Let us assume the sides of the triangle as √41,4,5.√41 be the longest side of the given triangle.


Right Triangle

Fig c :Right triangle
              AB2 = AC2 + BC2   

              ( √41)2  = 4+ 52
              ( √41)2  = 16 + 25
                    41  = 41

Since LHS is equal to RHS, the triangle is a right triangle.