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

  • question_answer
    The angles of depression of two ships from the top of the light house are \[45{}^\circ \] and \[30{}^\circ \] towards east. If the ships are 100 m apart. then the height of the light house is :

    A) \[50(\sqrt{3}-1)\,m\]                   

    B) \[50(\sqrt{3}+1)\,m\]

    C) \[50(\sqrt{3})\,m\]                      

    D) \[\frac{50}{\sqrt{3}-1}\,m\]

    Correct Answer: B

    Solution :

    Here let AB be the height of light house and D, C are the ships such that CD = 100m. Applying short cut method. \[AB=\frac{100}{\cot 30{}^\circ -\cot 45{}^\circ }\] \[\Rightarrow AB=\frac{100}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}\] \[AB=\frac{100(\sqrt{3}+1}{2}\] \[=50(\sqrt{3}+1)\] m


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