Concept preview

What you will be able to do

1. 01Label a triangle so each side $a, b, c$ is opposite its angle $A, B, C$.
2. 02State and apply the sine law $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$.
3. 03Use the sine law when you know two angles and a side, or two sides and a non-included angle.
4. 04Find an unknown side or angle in an oblique (non-right) triangle.
5. 05Recognise and resolve the ambiguous (SSA) case: zero, one, or two triangles.

Everything in the last topic depended on that convenient $90°$ corner — SOH-CAH-TOA simply has nowhere to grip without it. Yet most triangles you meet in surveying a plot of land, plotting a ship's course, or bracing a roof truss are oblique: they have no right angle anywhere. We need a tool that works on any triangle, and the first of two such tools is the sine law. It rescues exactly the situations where right-triangle trig gives up.