10th Class Mathematics Solved Paper - Mathematics 2017 Outside Delhi Set-III

  • question_answer From the top of a tower, 100 m high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angles of depression \[30{}^\circ \] and \[45{}^\circ \]. Find the distance between the cars. [Take \[\sqrt{3}=1.732\]]

    Answer:

    Let AB is a tower.
    Cars are at point C and D respectively
    In \[\Delta \,ABC\],
                                        \[\frac{AB}{BC}=\tan \,\,30{}^\circ \]
                                        \[\frac{100}{x}=\frac{1}{\sqrt{3}}\]
                                            \[x=100\sqrt{3}\]
                                               \[=100\times 1.732\]
                                                \[=173.2\,\,m\]
    In \[\Delta \,ABD\],
                                        \[\frac{AB}{BD}=\tan \,\,45{}^\circ \]
                                        \[\frac{100}{y}=1\]
                                            \[y=100\,m\]
    Distance between two cars \[=x+y\]
    \[=173.2+100\]
    \[=273.2\,m\]


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