Sine rule and cosine rule (Pure Maths) — A/L Combined Mathematics

How do I practise Sine rule and cosine rule (Pure Maths)?

1 question with a worked solution

1. In any triangle ABC with circumradius R and standard notation, which of the following expresses the area Δ of the triangle?
   1. A) Δ = (a b c) / (4R)
   2. B) Δ = 2 R² sin A sin B sin C
   3. C) Δ = (a + b + c) / (2R)
   4. D) Δ = (a b c) / (2R)
   Check my answer

   Correct answer: A) Δ = (a b c) / (4R)

   Area of triangle Δ = ½ a b sin C. From the Sine Rule, c / sin C = 2R => sin C = c / (2R). Substituting gives Δ = ½ a b [c / (2R)] = (a b c) / (4R).

   Show worked solution

   Step 1: Δ = ½ a b sin C. Step 2: Sine Rule: sin C = c / (2R). Step 3: Δ = ½ a b (c / 2R) = abc / (4R). Answer: Δ = (a b c) / (4R).
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Sine rule and cosine rule (Pure Maths) fit in the syllabus?

Year 1 · Term 2