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

  • question_answer The angle of elevation of the top of a hill at the foot of a tower is \[60{}^\circ \] and the angle of elevation of the top of the tower from the foot of the hill is \[30{}^\circ \]. If height of the tower is 50 m, find the height of the hill.

    Answer:

    Let AB be hill and DC be tower.
    From\[\Delta \text{ }ABC\]                      \[\frac{AB}{BC}=\tan \,\,60{}^\circ \]
                                           \[h=BC\,\,\tan \,\,60{}^\circ =\sqrt{3}\,\,BC\]
    From \[\Delta \,DBC,\frac{DC}{BC}=\tan \,\,30{}^\circ =\frac{1}{\sqrt{3}}\]
    \[\Rightarrow \]               \[BC=\sqrt{3}\,\,DC=50\sqrt{3}\]
                            \[h=BC\sqrt{3}\]
                            \[=50\sqrt{3}\times \sqrt{3}=50\times 3\]
                            \[=150\,\,m\]


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