Sine and Cosine Rules summary

Key learning points

• Sine rule: ASA, AAS, or SSA (ambiguous case care).
• Cosine rule: SAS (find side) or SSS (find angle).
• Area $=\tfrac12 bc\sin A$ when you know two sides and the included angle.

Worked example 1 — Cosine rule side

$b=5$, $c=6$, $A=60^\circ$. Find $a$.

Working

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

Worked example 2 — Sine rule

$a=7$, $A=30^\circ$, $B=45^\circ$. Find $b$.

Working

$\frac{a}{\sin A}=\frac{b}{\sin B}$.

Worked example 3 — Area

Sides $5$, $6$, included angle $30^\circ$. Area?

Working

$\tfrac{1}{2}bc\sin A$.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.