Pythagorean Theorem or Pythagoras theorem was given by Pythagoras of Samos who was an ancient Ionian Greek Philosopher. Pythagoras Theorem is a Mathematical relation between the slides of a right-angled Triangle.

**Right Angled Triangle:** A right angle Triangle or a right-angled triangle is a triangle that is at one angle is a right angle or a 90° angle. The side opposite to the angle is called the hypotenuse and the sides adjacent to the right angle are called base and height.

This is a right-angled triangle, and from the figure, we can see that the side opposite to the right angle is the hypotenuse.

A right-angled triangle is the basis of all trigonometric operations.

Coming back to Pythagoras theorem, so as mentioned earlier Pythagoras theorem is a relation between the sides of a right-angle triangle. The square of the hypotenuse of the triangle is equal to the sum of the square of height and base of the triangle.

Mathematically formula for the Pythagorean theorem is (Hypotenuse)^{2} =(Base) ^{2}+ (Height)^{2}

For Example, a right angle triangle with a height of 4cm and a base of 3cm find the hypotenuse of the triangle.

So we a triangle with base=3cm and height=4cm,

Therefore, using Pythagoras theorem

(Hypotenuse)^{2} =(Base) ^{2}+ (Height)^{2}

(Hypotenuse)^{2} =(3) ^{2}+ (4)^{2}

(Hypotenuse)^{2} = 9 + 16

(Hypotenuse)^{2} =25

** Hypotenuse = 5**

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**FREQUENTLY ASKED QUESTIONS**

**What is Pythagoras Theorem?**

Pythagoras Theorem is a relationship between the sides of a right-angle triangle. The formula for Pythagorean theorem

(Hypotenuse)^{2} =(Base) ^{2}+ (Height)^{2}

2. **How can we find the base of a right triangle if we have the hypotenuse and height of the Triangle?**

To find the base of a triangle whose hypotenuse and base are known we can use the formula for the Pythagorean theorem in such a way.

For eg. we have a triangle with hypotenuse 7 and height 5 then the base of the triangle is given by:

(Base)^{2} =(Hypotenuse) ^{2}– (Height)^{2}

(Base)^{2} =(7) ^{2}– (5)^{2}

(Base)^{2} = 49 – 25

(Base)^{2} =24

Base =**√24**

Base =4.8

**3. What is the formula to determine the area of a right-angle triangle?**

The Area of a right angle triangle is given by:

Area=(Base * Height)/2

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