My solution is above, including the question. When I was spending spring afternoons in the pavilion doing maths homework, I hit on the idea of only using the sine ratio, Pythagoras’ result and the sine rule to solve these problems as it reduced the amount of things I needed to remember. I’ve used sine rule in the large triangle and then found the inclination of the road. This was a nostalgic exercise, and, as a result of not being able to find my Godfrey and Siddons or a scientific calculator to hand, I found myself using Wolfram Alpha to look up the trig ratios.

Steve Nicholson’s solution from daringfireball.net. This solution has gone for ‘projecting’ the pole shadow onto the horizontal and then solved the small triangle using sine rule.