The Sine and Cosine Rules (Edexcel GCSE Maths): Flashcards

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The sine and cosine rules
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Use of sine & cosine rules

Non-right-angled triangles

Letter case for sides in triangle labelling

Lowercase

Letter case for angles in triangle labelling

Uppercase

Side-angle relationship in labelling

Each side has same letter as opposite angle

Sine rule formula

asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Cosine rule to find a side

a2=b2+c22bccosAa^2 = b^2 + c^2 - 2bc \cos A

Cosine rule to find an angle

cosA=b2+c2a22bc\cos A = \frac{b^2 + c^2 - a^2}{2bc}

Area with 2 sides & enclosed angle

12absinC\frac{1}{2}ab \sin C

Rule when: 2 angles & any side

Sine rule

Rule when: 2 sides & non-enclosed angle

Sine rule

Rule when: 2 sides & enclosed angle

Cosine rule

Rule when: 3 sides, no angles

Cosine rule

Warning for sine rule with 2 sides & non-enclosed angle

Ambiguous case - may have 2 solutions

Sum of triangle angles

180°

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