Pythagorean Learning

Pythagorean Theorem states that, “In any right angle triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle)”.

Pythagorean Theorem is applied only, when the given triangle is a right angle triangle. I like to share this Pythagorean Identity with you all through my article.


General equation of Pythagorean Theorem

The theorem can be written as an equation,

c^2 =a^2+ b^2

Where c denote the length of the hypotenuse, and a and b represent the lengths of the other two sides.

If we let 'c' be the length of the hypotenuse and 'a' and 'b' is the lengths of the other two sides, the theorem can be expressed as the equation:

c^2 =a^2+ b^2

Or, solved for c:

c=square root of (a^2+b^2)

If c is given, and the length of one of the side must be found, the following equations (which are corollaries of the first) can be used:

c^2 -a^2= b^2

Or

c^2 - b^2 = a^2

This equation gives a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found. An overview of this theorem is the law of cosines, which allows the computation of the length of the third side of any triangle, given the lengths of two sides and the size of the angle between them. If the angle between the sides is a right angle it will be reduces to the Pythagorean Theorem. Understanding andhra pradesh board of secondary education is always challenging for me but thanks to all math help websites to help me out.


How to solve the right triangle using Pythagorean


Example:

Find the length of a side 'a' in the right triangle, if b = 9 and c=15.

Solution:

We know that formula,

c^2 =a^2+ b^2

We need to find the value of 'a' so,

a^2=c^2- b^2

a^2= (15)2 – (9) 2

a^2 = 225 -81

a^2=144

Take square on both sides,

a =12

The side a value is 12.