Area, Sine, and Cosine Rules (Grade 11 NSC Matric Mathematics): Flashcards

$\text{Area} = \frac{1}{2}bc \sin A$

Two sides and the included angle known

Angle that lies between two known sides

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Two angles + one side, or two sides + non-included angle

Two possible triangles satisfy given conditions

$a^2 = b^2 + c^2 - 2bc \cos A$

Two sides + included angle, or all three sides known

$\cos A = \frac{b^2 + c^2 - a^2}{2bc}$

Becomes Pythagoras' theorem: $a^2 = b^2 + c^2$