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    Question

    In a right angle triangle, the product of two sides is half of the square of the third side (i.e., hypotenuse). Accordingly find out the acute angle?

    A 45 Correct Answer Incorrect Answer
    B 60 Correct Answer Incorrect Answer
    C 30 Correct Answer Incorrect Answer
    D None of these Correct Answer Incorrect Answer

    Solution

    According to the question, BC×AB = 1/2AC2  -----(1) BC2 + AB2 = AC2 -----(2) by Pythagoras Putting the value of AC2 in equation (2), BC2 + AB2  = 2BC × AB Or BC2 + AB2 - 2BC × AB = 0 Or (BC – AB)2 = 0 Or BC – AB  = 0 Or BC = AB  Hence ∠BAC = ∠BCA = 45 (As sum of two angles other right angle in a right angle triangle is 900).

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