- 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 states that the longest side in a right-angled triangle is called the
**hypotenuse**- The hypotenuse will always be the side
**opposite**the right angle

- The hypotenuse will always be the side
- If we label the hypotenuse c, and label the other two sides a and b then Pythagoras’ Theorem tells us that:
**a**Where a, b, and c are the lengths of the three sides^{2}+ b^{2}= c^{2}

- To find the length of the
**hypotenuse**use- This is just a rearrangement of the formula
**a**, to make^{2}+ b^{2}= c^{2}**c**the subject - Note that when finding the hypotenuse you
**add**inside the square root

- This is just a rearrangement of the formula
- To find the length of
**one of the other sides**use**or**- This is a rearrangement of the formula
**a**, to make either^{2}+ b^{2}= c^{2}**a**or**b**the subject - Note that when finding one of the shorter sides you
**subtract**inside the square root

- This is a rearrangement of the formula

- ‘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

In the following diagram:

is a straight line, with
and

Find , the length of side Give your answer to 1 decimal place.

To find
, we first need to find the length of
using triangle

Note that
is a shorter side

It is best to leave rounding until the very end, use in subsequent working

Now we can find using triangle

Round to 1 decimal place

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