Trigonometry: Sine, Cosine and Area Rules notes

This section solves a right-angled triangle in a 2D context with **$\sin$,$\cos$and$\tan$: SOH CAH TOA. From the two knowns and the unknown you choose the ratio, then find a side or an acute angle. Degrees…

This section finds the area of any triangle from two sides and the included angle: $\dfrac{1}{2}ab\sin C$, and the two cyclic twins. Drop a perpendicular to derive it. When the included angle is obtuse, $\sin$…

This section finds a missing side or a missing angle in any triangle with the sine rule: $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$. Pair each side with the angle opposite it. Use the triangles and lengths this…

This section finds a missing side or a missing angle in any triangle with the cosine rule: $a^{2}=b^{2}+c^{2}-2bc\cos A$ (and cyclic). Use two sides and the included angle (SAS) to find the third side, or…

This section solves 2D and 3D triangles by combining right-triangle ratios, the area rule, the sine rule and the cosine rule. Sketch the situation, then draw the 2D net of every 3D pair: a vertical…