Learning pack · IGCSE handout

Sine and Cosine Rules

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). For non-right triangles: sine rule $\frac{a}{\sin A}=\frac{b}{\sin B}$ , cosine rule $a^2=b^2+c^2-2bc\cos A$ .

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Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

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Files: 44_sine_and_cosine_rules_handout.pdf · 44_sine_and_cosine_rules_handout_answers.pdf

Full topic summary

For non-right triangles: sine rule $\frac{a}{\sin A}=\frac{b}{\sin B}$ , cosine rule $a^2=b^2+c^2-2bc\cos A$ .

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=\sqrt{31}

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

Worked example 2 — Sine rule

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

Working

b=7\sqrt{2}

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

Worked example 3 — Area

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

Working

7.5

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

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