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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-7

  • question_answer
    In an acute angled triangle ABC, if sin 2(A + B - C) = 1 and tan \[\left( B+C-A \right)\]= \[\sqrt{3}\]. then the value of \[\angle \]B is

    A) \[60{}^\circ \]                          

    B) \[30{}^\circ \]

    C) \[52\frac{1}{2}{}^\circ \]

    D)  \[67\frac{1}{2}{}^\circ \]

    Correct Answer: C

    Solution :

     sin2 \[\left( A+B-C \right)=1\] = sin \[90{}^\circ \] \[\Rightarrow 2\left( A+B-C \right)=90{}^\circ \] \[\Rightarrow A+\text{ }B-C=45{}^\circ \]                      .....(i) \[\tan \,(B+C-A)=\sqrt{3}\] = tan \[60{}^\circ \] \[\Rightarrow B+C-A=60{}^\circ \]                     ..... (ii) On adding both the equations, \[A+B-C+B+C-A\] \[=45{}^\circ +60{}^\circ \] \[\Rightarrow 2B=105{}^\circ \Rightarrow B=52\frac{1{}^\circ }{2}\]


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