Analysis of Pythagorean Theorem

Pythagorean Theorem is one of the most fundamental theorems in mathematics and it defines the relationship between the three sides of a right-angled triangle. You are already aware of the definition and properties of a right-angled triangle. It is the triangle with one of its angles as a right angle, that is, 90 degrees. The side that is opposite to the 90-degree angle is known as the hypotenuse. The other two sides that are adjacent to the right angle are called legs of the triangle.

  The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.

In a right-angled triangle, the total sum of the individual squares of the base and altitude would be equal to the square of the length of the hypotenuse.

Let us denote the base of the right-angled triangle as letter ‘b’, the altitude of the triangle as ‘a’ and hypotenuse of the same triangle as the letter ‘h’, then as per the Pythagoras theorem

h² = b² + a²

The numerical triplets which would satisfy this formula are termed as Pythagorean triples. The numerical triplets like (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), etc. comes under the category of Pythagorean triplets. The multiples of these basic triplets also behave like a normal triplet, and if considered (a, b, c) as a basic Pythagorean triplet then the multiple of these triplets (ka, kb, kc) also comes under the category of the Pythagorean triplet. It should be noted that the constant ‘k’ in this context is a non-negative integer.

Application of Pythagoras Theorem in Real Life

The following are the applications of the Pythagoras theorem:

• Pythagoras theorem is used to check if a given triangle is a right-angled triangle or not. 
• Aerospace scientists and meteorologists find the range and sound source using the Pythagoras theorem.
• It is used by oceanographers to determine the speed of sound in water

• What is the use of Pythagoras Theorem?

  The Pythagoras theorem, also known as Pythagorean theorem is used to find the sides of a right-angled triangle. This theorem is mostly used in Trigonometry, where we use trigonometric ratios such as sine, cos, tan to find the length of the sides of the right triangle.

• What is the real-life application of Pythagoras Theorem Formula?

  The length of diagonal connecting two buildings can be calculated using this formula.

  Also, we use this formula along with trigonometry concept, to find the angle of elevation if a person seeing an object kept at top of the building with respect to the horizontal line. The angle of depression is calculated when the object is kept below the line of sight of the person..

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