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JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Relation between sides and angles, Solutions of triangles

  • question_answer
    In triangle ABC and DEF, AB = DE, AC = EF and \[\angle A=2\angle E\]. Two triangles will have the same area, if angle A is equal to

    A) \[\frac{\pi }{3}\]

    B) \[\frac{\pi }{2}\]

    C) \[\frac{2\pi }{3}\]

    D) \[\frac{5\pi }{6}\]

    Correct Answer: C

    Solution :

    It is given that area of \[\Delta ABC=\]Area of \[\Delta DEF\] Þ \[\frac{1}{2}(AB)(AC)\sin A=\frac{1}{2}(DE)(EF)\sin E\] Þ \[\sin A=\sin E\Rightarrow \sin 2E=\sin E\Rightarrow 2E=\pi -E\] Þ \[E=\frac{\pi }{3}\Rightarrow A=2E=\frac{2\pi }{3}\].


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