# 4.8.1 Pythagoras Theorem

#### What is Pythagoras?

• Pythagoras was a Greek mathematician who lived over 2500 years ago
• He is most famous for Pythagoras’ Theorem, which includes the important formula for right-angled triangles

#### Pythagoras’ theorem?

• The longest side in a right-angled triangle is called the hypotenuse – this will always be the side opposite the right angle
• If we label the hypotenuse c, and label the other two sides a and b: then Pythagoras’ Theorem tells us that:
a2 + b2 = c2
(where a, b, and c are the lengths of the three sides)

#### Using Pythagoras’ theorem

• To find the length of the hypotenuse use:
c = √a2 + b2
(Note that when finding the hypotenuse you add inside the square root)
• To find the length of one of the other sides use:
a = √c2 – b2 or b = √c2 – a2
Note that when finding one of the other sides you subtract inside the square root

#### Exam Tip

If your calculator gives you a ‘Math ERROR’ result, you probably subtracted the wrong way around in the square root.

In questions with multiple steps, don’t round off (to 1 decimal place, 3 significant figures, etc) until the very end.

### Worked Example

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