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Geometry & Trigonometry

Sine & Cosine Rules

Choose the correct rule, connect sides with their opposite angles and solve non-right-angled triangles.

Curriculum rangeYears 10–11

Given two angles and a side, find the other sides.

ABCA = 50°B = 70°a = 8b = 9.8c = 9
asin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

C=180∘−50∘−70∘=60∘C=180^\circ-50^\circ-70^\circ=60^\circ

b=asin⁡Bsin⁡A=8sin⁡(70°)sin⁡(50°)=9.8b = \dfrac{a \sin B}{\sin A} = \dfrac{8\sin(70°)}{\sin(50°)} = 9.8
c=asin⁡Csin⁡A=8sin⁡(60°)sin⁡(50°)=9c = \dfrac{a \sin C}{\sin A} = \dfrac{8\sin(60°)}{\sin(50°)} = 9