You are shown a diagram of a right angled triangle, with the hypotenuse labelled c and the other sides labelled a and b. If a is 7m long and c is 10m long, what is the length of b?

A simple implementation of Pythagoras' Theorem a²+b²=h², and as in the question c is the hypotenuse, a²+b²=c². (Side Note - in exams, the question may not specify which length is the hypotenuse - this is always the longest length of the triangle!)

 To get the length b, the formula must be rearranged so that we have something of the form 'b=...'. In order to do this, we must subtract 'a²' from the left hand side (LHS) of the equation, but to preserve the equality (the equals sign) a² must be subtracted from the right hand side (RHS) too. This gives b²=c²-a². Finally, both sides must be square rooted, so we have b=(c²-a²)^1/2 (Side Note - something to the power of a half is the same as square rooting it!). Putting in the numbers, we are left with 7.141m. (Remember - UNITS!)