4.8cHigher tier1MA1 · Section 4: Geometry and trigonometry

Sine rule, cosine rule, area = ½·ab·sinC

Key learnings

Choose the rule from what you are given
Right-angled → SOHCAHTOA (sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj). Otherwise: a matching side–angle pair → sine rule; two sides + the included angle (SAS — Side-Angle-Side) or all three sides (SSS — Side-Side-Side) → cosine rule.
The formulae (all on the formula sheet)
Sine rule $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$ ; cosine rule $a^2=b^2+c^2-2bc\cos A$ ; area $=\tfrac12 ab\sin C$ with $C$ the angle between $a$ and $b$ .

Drawn from real examiner reports.

Quoting the sine or cosine rule incorrectly

Even though both are on the formula sheet, students copy them down wrongly.

Rearranging the area/cosine formula wrongly

Algebra slips when solving $\tfrac12 ab\sin C$ for a side, or the cosine rule for an angle.

For area, C must be the angle between the two sides

Using a non-included angle (not between $a$ and $b$ ) in $\tfrac12 ab\sin C$ .

Write the formula, substitute, then rearrange
Quoting the rule and showing the substitution earns method marks; keep full accuracy to the end.

You have…	Use
A right angle	SOHCAHTOA (sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj)
A side and its opposite angle (+ one more)	Sine rule
Two sides and the included angle (SAS — Side-Angle-Side)	Cosine rule (for the third side)
All three sides (SSS — Side-Side-Side)	Cosine rule (for an angle)
Two sides and the included angle	Area $=\tfrac12 ab\sin C$

Core

Cosine rule rearranged to find an angle A from three sides a, b, c — what is the formula?

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