A ladder 6·8m long is leaning against a wall, as shown in the diagram. The foot of the ladder is 1·5m from the wall. Calculate the distance the ladder reaches up the wall. Give your answer to a sensible degree of accuracy.

There's a lot of information here so we should start out by drawing up a diagram. From this we can see that we have a right-angled triangle, and we know two of the angles and want to work out a third. Therefore we must use Pythagoras' theorem (this would be described in full on a whiteboard): a^2 + b^2 = c^2. We have c (6.8m) and we have b (1.5). Putting these into the question we have a^2 + 1.5^2 = 6.8^2. To answer the question we must work out a. We do this by rearranging the equation we have. a^2 = 6.8^2 - 1.5^2. Therefore to get a we must square root the equation. Root(6.8^2 - 1.5^2) =6.63249575952. Since all other values in the question are given to one decimal place, we should also give our answer to one decimal place. Therefore: a = 6.6m