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    Question

    If in triangle ABC, If side AB=6√ 3, AC=12 and BC=6,

    then angle B equals:
    A 120° Correct Answer Incorrect Answer
    B 60° Correct Answer Incorrect Answer
    C 90° Correct Answer Incorrect Answer
    D 45° Correct Answer Incorrect Answer

    Solution

    In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.   In ΔABC AB = 6√3 cm; AC = 12 cm; BC = 6 cm AB2 = 108 cm2; AC2 = 144 cm2; BC2 = 36 cm2 AB2 + BC2 = (108 + 36) cm2 = 144 cm2 ⇒ AC2 = AB2 +BC2 Pythagoras theorem satisfied. Thus, ∠ABC = 90°

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