The sides of right-angled triangles are labelled opposite, hypotenuse and adjacent. Trigonometry explores the relationship between sides and angles in right-angled triangles. The hypotenuse is the ...

So we've reduced the question to showing that sin(54°) = φ/2. The trick now is to consider the isosceles triangle ABC shown below, whose angles are 36°, 72° and 72°.