Using the sine and cosine rules together (AQA GCSE Further Maths): Flashcards

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Using the sine and cosine rules together
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Rule to use when you have all three side lengths

Cosine rule

Rule to use with two sides and included angle

Cosine rule

Rule to use with two angles and one side

Sine rule

Rule to start with: two sides, non-included angle

Sine rule

Independent measurements needed to solve any triangle

Three

Cosine rule formula to find side aa

a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc \cos A

Cosine rule formula to find angle AA

cos⁡A=b2+c2−a22bc\cos A = \frac{b^2 + c^2 - a^2}{2bc}

Sine rule formula

sin⁡Aa=sin⁡Bb=sin⁡Cc\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

Area formula for triangle with sides aa, bb, angle CC

12absin⁡C\frac{1}{2}ab \sin C

Direction bearings are measured from

Clockwise from North

Why three angles alone can't solve a triangle

Not independent; third angle determined by first two

Potential issue with sine rule (two sides, non-included)

Ambiguous case - two possible solutions

First step before solving any triangle problem

Draw a diagram

Why keep intermediate values in calculator

Rounding too early causes significant errors

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