In a triangle ABC, AB = AC. The length of the median from A to BC is 9 cm and the angle between the median and AB is 60°. Find the length of AB.
Let AB = AC = x. The length of the median is given as 9 cm, and the angle between the median and AB is 30°. Using the cosine rule in triangle AMB, where M is the midpoint of BC: AM² = AB² + BM² - 2 × AB × BM × cos 60°. AM = 9, BM = BC/2 = x/2. Substituting the values: 9² = x² + (x/2)² - 2 × x × (x/2) × cos 60°, 81 = x² + x²/4 - x².1/2. x² = 54 x = 7.35 Answer: b) 7.35 cm.
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