Pythagorean Theorem Calculator

**Pythagoras theorem calculator**

**What is Pythagoras theorem?**

Pythagoras theorem is in relation to geometry of right angle triangles. Right angle triangle is the one with 90^{o }angle in it. Pythagoras theorem is one of the earliest theorems known named after the mathematician Pythagoras.

Theorem states that the square of the hypotenuse is equal to the sum of squares of length of both the sides of the triangle. But the theorem is applicable only in case of right angle triangle and the side opposite to the right angle is longest which is called as hypotenuse.

**Formula-**

To calculate the hypotenuse of a triangle ABC, the formula is –

c^{2 }= a^{2 }+ b^{2}

Where, c is the side opposite to right angle

a and b are the other to legs of the right angle triangle.

Thus, if you know length of any two sides of the triangle, you can calculate the third side of the triangle.

**Application of theorem-**

- To calculate the third side of the triangle, if two sides are known.
- To calculate the diagonal of a square.
- To know if the triangle is right angle triangle.

**How to use manually-**

The formula is c^{2 }= a^{2 }+ b^{2}

Where, ‘c’ is the hypotenuse, ‘a’ is the perpendicular side and ‘b’ is base.

For example- In a right angle triangle ABC, side a=3cm, b=4cm. Calculate the hypotenuse?

Solution- Using the formula- c^{2 }= a^{2 }+ b^{2}

And substituting the value in the formulae-

c^{2 }= 3^{2 }+ 4^{2}

c^{2} = 9 + 16

c^{2} = 25

c =

c = 5

Hence, the third side is 5cm.

You can also use the formula to check whether the triangle is right angle triangle or not. Following example is to explain the method to check the type of triangle. Consider a triangle whose sides are 12, 5 and 13.

We know, the longest side is considered as hypotenuse and hence, let’s consider c= 13, a= 12 and b= 5

We have the formula, c^{2 }= a^{2 }+ b^{2}

Substituting the value, 13^{2} = 12^{2} + 5^{2}

169= 144 + 25

169 = 169

Hence, RHS = LHS, which means that side c is hypotenuse and the triangle is a right angle triangle.

**How to use the calculator-**

- To use the calculator, you must have the lengths of the sides of right angle triangle. Pythagoras theorem calculator doesn’t support the calculation for other triangles.
- Enter the input values of any two sides of the triangle.
- Press the enter button to know the results.
- You can add value of hypotenuse and perpendicular or hypotenuse and base or any combination to find the value of rest leg.
- The Pythagoras theorem will always provide the value of third side.

**Note-**

- A length is always a positive number and hence the result will always be positive from the calculator.
- The input values should be a real positive number.
- The longest side is always considered as the hypotenuse.
- It is important that the triangle should be the right angle triangle only.