JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Critical Thinking

  • question_answer
    If the sides of a \[\Delta \]be\[({{x}^{2}}+x+1),\,(2x+1)\] and \[({{x}^{2}}-1),\]then the greatest angle is   [EAMCET 1987; Kerala (Engg.) 2001]

    A) \[{{105}^{o}}\]

    B) \[{{120}^{o}}\]

    C) \[{{135}^{o}}\]

    D) None

    Correct Answer: B

    Solution :

    Sides are\[({{x}^{2}}+x+1),\,(2x+1),\,({{x}^{2}}-1)\]. The greatest side subtends the greatest angle. Hence \[{{x}^{2}}+x+1\] is the greatest side. Now \[\cos \theta =\frac{{{(2x+1)}^{2}}+{{({{x}^{2}}-1)}^{2}}-{{({{x}^{2}}+x+1)}^{2}}}{2(2x+1)({{x}^{2}}-1)}\] \[\Rightarrow \] \[\theta ={{120}^{o}}\].


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