Stage: 5 Challenge Level: 
Why do this problem?
Use the cosine rule to find exact values for the cosines of 36 degrees and 72 degrees.
Possible approach
Introduce this problem as one of a collection of problems involving the Golden Ratio.
See Golden Trail 1 .
Key question
If you have no right angles triangles how do you introduce the cosine?
Ruler & protractor constructions. Fibonacci sequence. Surds. Pentagons. Rhombi. Mathematical reasoning & proof. Quadratic equations. Angle properties of shapes. Golden ratio. Mixed trig ratios.
Published November 2000.
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