**The Pythagorean theorem in practice**

As the name suggests, the Pythagorean theorem is attributed to Pythagoras. He was an ancient Greek mathematician and philosopher who contributed significantly to the development of science, and we still use his mathematical theorem today.

**Pythagoras' theorem - applications**

This theorem is most commonly used when we know two of the three side lengths of a right-angled triangle in order to calculate the length of the remaining unknown. In other words, Pythagoras' theorem is as follows:

if the triangle is right-angled, the sum of the squares of the two perpendicular sides is equal to the square of the hypotenuse.

**Pythagoras' theorem - the formula**

To put Pythagoras' theorem into practice, you will need a mathematical formula. It looks as follows: a^2 + b^2 = c^2, where the letters ‘a’ and ‘b’ symbolise the perpendicular sides and the letter ‘c’ symbolises the side of the hypotenuse.

**Pythagoras' theorem - an example using the formula**

Imagine a right-angled triangle with perpendicular sides of 3cm and 4cm, and a hypotenuse of unknown length which we want to calculate. Using the mathematical formula in practice would be as follows:

3^2 + 4^2 = c^2

9 + 16 = c^2

25 = c^2

5 = c

In this way, we have easily calculated the unknown length of the hypotenuse of a right-angled triangle. In order to use the formula correctly and solve the problem efficiently, you only need to remember to substitute the numbers correctly for the letters. You will also need to know about powers and roots, which are the foundation of Pythagoras' theorem.

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