How do I work out the length of sides on a right-angle triangle?

Over 2000 Pythagoras discovered that when a triangle has a right angle (90 degrees), and squares are made for each of the three sides, then the biggest square has the exact same area as the two other squares put together. 

The equation is called Pythagoras Theorem: a²+b² = c²  (c is the longest side of the triangle, a and b are the shorter sides)

For example:

Let's check if the areas are the same:

3² + 4² = 5²

Calculating this becomes:

9 + 16 = 25 

In most GSCE questions you are given the length of at least 2 sides to the triangle. You can then use this formular to work out the third side. 

For example:

Lets say a=9 and c=15

Put in what we know: 9² + b² = 15²

Calculate squares: 81 + b² = 225

Take 81 from both sides: 81 − 81 + b² = 225 − 81

Calculate: b² = 144

Square root of both sides: b = √144

Calculate:b = 12