Non-Right-Angle Trigonometry
Use the sine rule, cosine rule and area formula.
Formula booklet essentials
Sine rule\[ rac a{\sin A}= rac b{\sin B}= rac c{\sin C}\]
Cosine rule\[a^2=b^2+c^2-2bc\cos A\]
Area\[ ext{Area}= rac12ab\sin C\]
Worked example
In triangle ABC, \(a=7\), \(b=9\), and \(C=40^\circ\). Find the area.
\[ ext{Area}= rac12ab\sin C= rac12(7)(9)\sin40^\circpprox20.2.\]