Sine rule and cosine rule — A/L Combined Mathematics

How do I practise Sine rule and cosine rule?

1 question with a worked solution

1. In a triangle ABC, sides b = 3 cm, c = 5 cm, and angle A = 60°. Using the Cosine Rule, what is the exact length of side a?
   1. A) √34 cm
   2. B) 4 cm
   3. C) √19 cm
   4. D) √49 cm (7 cm)
   Check my answer

   Correct answer: C) √19 cm

   By the Cosine Rule: a² = b² + c² - 2bc cos A. Substituting b = 3, c = 5, A = 60° (cos 60° = 1/2): a² = 3² + 5² - 2(3)(5)(1/2) = 9 + 25 - 15 = 19. Hence, a = √19 cm.

   Show worked solution

   Step 1: Formula: a² = b² + c² - 2bc cos A. Step 2: a² = 9 + 25 - 2(3)(5)(0.5) = 34 - 15 = 19. Step 3: a = √19 cm. Answer: √19 cm.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Sine rule and cosine rule fit in the syllabus?

Year 1 · Term 2