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All 9 Flashcards — Sine & cosine rules
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Question
State the sine rule.
Answer
a/sinA = b/sinB = c/sinC (side over the sine of its opposite angle).
Question
State the cosine rule for a side.
Answer
a² = b² + c² − 2bc·cosA, with A opposite a.
Question
Cosine rule rearranged for an angle?
Answer
cos A = (b² + c² − a²)/(2bc).
Question
When do you use the sine rule?
Answer
When you have a side with its opposite angle, plus one more side or angle.
Question
When do you use the cosine rule?
Answer
For SAS (two sides + included angle → third side) or SSS (three sides → an angle).
Question
How do you use the sine rule to find an angle?
Answer
Flip it: sinA/a = sinB/b, so the unknown sine is on top.
Question
Why is the cosine rule 'Pythagoras with a correction'?
Answer
When A = 90°, cosA = 0 and a² = b² + c².
Question
No side–opposite-angle pair — which rule first?
Answer
The cosine rule — it usually gives you a pair to then use the sine rule.
Question
SAS triangle: b=7, c=9, A=60°. Find a.
Answer
a² = 49 + 81 − 2·7·9·½ = 67 ⇒ a ≈ 8.19.
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Sine & cosine rules
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