# Pythagoras Theorem:

Pythagoras theorem is an important concept used while solving problems in mathematics. This theorem establishes the relationship between the sides of a triangle.

The Pythagorean theorem was originated by Pythagoras, a Greek philosopher of the 6th century BCE, who declared it to be an essential property of right-angled triangles.

Hence this theorem is named after him. If any triangle obeys the Pythagorean theorem, then it is definitely a right angled triangle.

Let’s take a look at the statement, formula, proof, application and examples of Pythagoras theorem.

## Pythagoras Theorem: Statements and Formulas:

In a right triangle, the side opposite the right angle is called the hypotenuse

and the other two sides are known as the base of the right triangle.

The hypotenuse is the longest side; And the other 2 sides are named as perpendicular and base.

### Statement of Pythagoras Theorem:

Pythagoras Theorem states that “in a right angled triangle, the square of the hypotenuse is equal to sum of the squares of the other two sides”

#### Formula of Pythagoras Theorem:

Pythagoras theorem can be written as:

AB² + BC² = AC²

Also it can ne written as:

AC² = AB² + BC²

or

AB² = AC² – BC²

or

BC² = AC² – AB²

or it can be written as:

H² = P² + B²

B² = H² – P²

P² = H² – B²

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Some Example have given below :

1.Example : Find the Value of H. if B = 100 mm and P = 80 mm.

we will use this formula for finding the H value:

H² = P² + B²

H² = 80² + 100²

H² = (80×80) + (100×100)

H² = 6400 + 10000

H² = 16400

H = √16400

H = 128.06 mm Ans.

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2.Example : Find the Value of B. if H = 100 mm and P = 70 mm.

we will use this formula for finding the B value:

B² = H² – P²

B² = 100² – 70²

B² = (100×100) – (70×70)

B² = 10000 – 4900

B² = 5100

B = √5100

B = 71.41 mm Ans.

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3.Example : Find the Value of P. if H = 100 mm and P = 70 mm.

we will use this formula for finding the P value:

P² = H² – B²

P² = 110² – 90²

P² = (110×110) – (90×90)

P² = 12100 – 8100

P² = 4000

P = √4000

P = 63.24 mm Ans.

Now if You want to calculate it by Calculator then simply Download Triangle Solver App from play store.https://play.google.com/store/apps/details?id=com.fitterkipurijankari.triangularsolver

Where we will apply this formula in the job?

when we get such type of job then there we apply this formual to find out the hyponuse value.

example is given below…

Now we will take measurement as shown above and then we will calculate Hypotenuse value. which will be our pipe length that pipe is called Travel pipe.

and then finally we will fabricate like this as shown in above picture.

But if you want to watch full tutorial video please visit our Youtube Channel Fitterkipurijankari.

Next we will learn How to calculate degree for miter cutting Click here.**Also Read.. Beam Miter cutting formula**