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    Question

    In a right angles trainagle, one acute angle is double the other. If the length of its hypotenuse is 20 cm, the find its area?

    A 50√3 cm² Correct Answer Incorrect Answer
    B 25√3 cm² Correct Answer Incorrect Answer
    C 60√3 cm² Correct Answer Incorrect Answer
    D 35√3 cm² Correct Answer Incorrect Answer

    Solution

    Let acute angle be x Other acute angle be 2x Sum of all the angles of triangle = 180° x + 2x + 90 = 180 3x = 90 x = 30 In ∆ABC sin60° = AC/BC 1/2 = BC/20 → BC = 10 cm cos60° = AB/AC →AB/20 √3/2 = AB/20 - AB = 10√3 Area of triangle = 1/2 × base × height = 1/2 × 10√3 × 10 = 50√3 cm²

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