Non-Right-Angle Trigonometry
Use the sine rule, cosine rule and area formula.
Formula booklet essentials
Sine rule\[\frac a{\sin A}=\frac b{\sin B}=\frac c{\sin C}\]
Cosine rule\[a^2=b^2+c^2-2bc\cos A\]
Area\[\operatorname{Area}=\frac12ab\sin C\]
Worked example
In triangle ABC, \(a=7\), \(b=9\), and \(C=40^\circ\). Find the area.
\[\operatorname{Area}=\frac12ab\sin C=\frac12(7)(9)\sin40^\circ\approx20.2.\]