Solution of Triangle

Having solved trigonometric equations, we now turn to a second classical application of trigonometry: relating the angles and sides of a triangle to each other so precisely that knowing any three elements (with at least one side) pins down every other element. Along the way we introduce polar co-ordinates, a second way of describing a point's position that turns out to be exactly the language needed to build these relations, and then derive the Sine Rule, Cosine Rule and Projection Rule — the three master identities from which every other tr …