Asked by: Sheila Davies, Worcester
On sunny days, it's easy: just measure the relative lengths of the shadows cast by the tree and yourself. The geometry of similar triangles then shows that if the shadow of the tree is X times longer than your shadow, then the tree is X times taller than you are.
On cloudy days, a bit more ingenuity is needed. Walk backwards from the base of the tree to a point where you can just cover the whole image of the tree with your hand held up vertically when your arm is fully outstretched. Then the theory of similar triangles, plus the relative lengths of average human hands and arms show that the height of the tree is roughly three times the distance you've walked from its base to reach this point.
Robert is a science writer and visiting professor of science at Aston University.