How do you work out the length of one of the sides of a right-angled triangle given the other two?

You must first identify which sides you are given. If you have been given both sides which are not the hypotenuse (the longest side opposite the ninety degree angle) then you can use the equation:

a^2 + b^2 = c^2

where a and b are the lenghts of the two sides you are given and c is the length of the hypotenuse. If you have been given one length and the hypotenuse then you simply rearrange the equation to a^2 = c^2 - b^2 where c is the hypotenuse and b is the other known side.

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