Pythagoras' theorem states that, for a right-angled triangle, the sum of the squares of the shorter sides = the square of the longest side (hypotenuse).
The basic formula for Pythagoras' theorem is: a2 + b2 = h2. The trouble is, the formula can be quite difficult to use. Instead, it's a lot better to just remember these three simple steps which work every time:

1. Square them:
Square the two numbers that you are given.
2. add or subtract:
To find the longest side, Add the two squared numbers. To find a shorter side, subtract the smaller one from the larger.
3. Square root:
Once you have got your answer, take the square root.

Trigonometry is also a part of Pythagoras' theorem. To do this you need to remember how the sides of a right-angled triangle are named, and the formulae for working out sine, cosine and tangent.
Basic rules:
SOH: Sine 0%= Opposite%Hypotenuse
CAH: Cosine 0%= Adjacent%Hypotenuse
TOA: Tangent 0%= Opposite%Adjacent

Using formula triangles to do trigonometry makes the whole thing a whole lot easier, but always follow all these steps in this order:

1. label the three sides of the triangle O (Opposite), A (Adjacent) and H (Hypotenuse).
2. Write down from memory 'SOH CAH TOA'
3. Decide which two sides are involved O,H A,H or O,A and select SOH CAH TOA accordingly.
4. Turn the one you choose into a formula triangle.
5. Cover up the thing you want to find with your finger, and write down whatever is left showing.
6. Translate into numbers and work it out.
7. Finally, check if your answer is sensible.

Four Nitty Gritty Details:

1. The hypotenuse is the longest side.
The opposite is the side opposite to the angle being used.
The Adjacent is the side next to the angle being used.
2. 0% is a Greek letter called 'theta', and is used to represent angles.
3. Always when working it out, use a diagram, draw your own if necessary.
4. You can only use SIN, COS and TAN on right-angled triangles - you may have to add lines to the diagram to create one - espacially on isosceles triangles.

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