We come across the concept of the Pythagoras theorem in various chapters of mathematics. It is a very important concept especially in the chapter on trigonometry. Pythagoras theorem is also sometimes referred to as Pythagorean theorem. Pythagoras theorem tells us that the sum total of the squares of the two sides of a right-angled triangle that are the base and the perpendicular is equal to the square of the hypotenuse of the triangle. The concept of the Pythagoras theorem makes it very easy for us to find out the different values of the trigonometric ratios in a right-angled triangle. In this article, we will discuss in detail the relationship between Pythagoras theorem and its relationship with the right-angled triangle. We will also discuss the history and the applications of the Pythagoras theorem.
What Do You Mean by the Right-Angled Triangle?
We know very well that a triangle has three angles. In a right-angled triangle, one of the angles of the triangles measures 90 degrees. This means that the other two angles of a right-angled triangle are always acute in nature which means that they measure less than 90 degrees. The famous mathematician Pythagoras found a very important relationship between the different sides of a right-angled triangle which we today know as the Pythagoras theorem.
Equation of Pythagoras Theorem
The Pythagoras theorem equation is very important since it will be used in various other topics of the subject. Without the understanding of this equation, you will not be able to solve a different set of problems. The Pythagoras theorem equation can be expressed as: z.z = x.x + y.y where x is the base of the right-angled triangle, y is the perpendicular or the height of the right-angled triangle and z is the hypotenuse of the right-angled triangle.
Let us take an example to understand the Pythagoras theorem equation more clearly.
Example: The hypotenuse of a right-angled triangle measures 10 units and one of the sides of the triangle measures 6 units. Find the measure of the remaining side of the triangle.
Solution: We know that the hypotenuse = 10 units and one of the sides of the triangle = 6 units.
Let the third side measure x units.
According to the Pythagoras theorem, Hypotenuse* Hypotenuse = Base* Base + Height* Height.
Thus, 10* 10 = 6* 6 + x* x
100 = 36 + x* x
x* x = 100 – 36
x* x = 64
x = 8
Thus, the measure of the remaining side of the triangle is 8 units.
History of Pythagoras Theorem
We came to know about this important theorem from the 4000-year-old Babylonian tablet. This tablet today is popularly known as the Plimpton 322. This theorem however was not popularized until Pythagoras came into the picture. Pythagoras lived during the 6th century BC. He was a mathematician and a philosopher who popularized this theorem in Italy, Egypt, and Babylon.
Various Applications of Pythagorean Theorem
We can find out the various applications of the Pythagorean theorem in our real life which are as follows:
- One of the most popular uses of the Pythagoras theorem can be seen in field excavations. Archeologists use this theorem to lay a precise grid system when they dig holes over the site in consideration. It is also used in the engineering and construction fields.
- You will be amazed to know that face recognition in mobile devices and computers uses the concept of the Pythagoras theorem.
- Architects and interior designers take the help of the Pythagoras theorem during the construction and design of different houses. Woodworkers also take the help of this theorem.
- Sailors use this theorem during their voyages to find out the shortest distance when they want to reach a particular place.
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