10th Class Mathematics Solved Paper - Mathematics-2018

  • question_answer As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are \[30{}^\circ \] and\[45{}^\circ \]. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use\[\sqrt{3}=1.732\]]


    Let AB be the light house and two ships be at C and D.
    In \[\Delta \text{ }ABC\],
                            \[\frac{BC}{AB}=\cot \,45{}^\circ \]
    \[\Rightarrow \]               \[\frac{x}{100}=1\]
    \[\Rightarrow \]               \[x=100\]                                              ...(i)
    Similarly, in \[\Delta \text{ }ABD\],
                            \[\frac{BD}{AB}=\cot \,\,30{}^\circ \]
    \[\Rightarrow \]               \[\frac{y}{100}=\sqrt{3}\]
    \[\Rightarrow \]               \[y=100\sqrt{3}\]                                               ?(ii)
    Distance between two ships \[=y-x\]
                                                    [from (i) and (ii)]
                            \[=100\left( \sqrt{3}-1 \right)\]


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