A ladder of length 5 m is place with the foot 2.2 m from the base of a vertical wall. How high up the wall does the ladder reach?

Drawing a diagram will help to visualise the problem and realise it is based on Pythagoras's theorem: a^2 + b^2 = c^2. We have been given 'c' the hypotenuse (5 m) and one of the shorter sides (2.2 m), which we shall say is 'b' leaving one unknown side (a).
We therefore need to rearrange the equation to make 'a' the subject: c^2 - b^2 = a^2. Now substitute in the numbers: 25-2.2 = a^220.16 = a^2. So 'a' is the square root of 20.16, which gives 4.49.
Don't forget the units! So the answer is the ladder will reach 4.49 m up the wall :)