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
- 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
‘Reality check’ your answers. If the hypotenuse ends up being shorter than another side in your answer, you’ve made a mistake somewhere!
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.