Stage: 4 Challenge Level: 
A cube (1 metre by 1 metre by 1 metre) has one face on the ground and one face pressed up to a wall. A ladder, 4 metre long, is leaning against the wall and it just touches the cube. How high is the top of the ladder above the ground?
Cosine rule. Circles. Mathematical reasoning & proof. Pythagoras' theorem. Gradients. Pythagorean triples. Long problems. Coordinates. Approximate solution by numerical methods.. Graphs.
Published November 1999.
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