In triangle ABC, side b = 8 cm, side c = 6 cm, and angle ∠A = 60°. Calculate the length of side a. (Take cos 60° = 0.5)
Answer and explanation
Correct answer: C. 7.21 cm (√52 cm)
- Step 1: Apply the Cosine rule: a² = b² + c² - 2bc cos A. Step 2. Substitute values: a² = 8² + 6² - 2(8)(6)(cos 60°) = 64 + 36 - 96(0.5) = 100 - 48 = 52. Step 3. Take square root: a = √52 ≈ 7.21 cm. Answer: 7.21 cm (√52 cm). Why not the others: 8.00 cm is side b; 10.00 cm is √100 (forgets -2bc cos A); 6.48 cm is an arithmetic error.
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