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

  • question_answer
    If in a triangle \[ABC,\]\[(s-a)(s-b)=s\,\,(s-c)\], then  angle C is equal to [MP PET 1986]

    A) \[{{90}^{o}}\]

    B) \[{{45}^{o}}\]

    C) \[{{30}^{o}}\]

    D) \[{{60}^{o}}\]

    Correct Answer: A

    Solution :

    \[\tan \frac{C}{2}=\sqrt{\frac{(s-a)(s-b)}{s(s-c)}}=1\]\[=\tan \left( \frac{\pi }{4} \right)\], from given data. Hence\[C={{90}^{o}}\].


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