10th Class Mathematics Solved Paper - Mathematics-2016 Delhi Term-II Set-II

  • question_answer The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are \[60{}^\circ \] and \[30{}^\circ \] respectively. Find the height of the tower.

    Answer:

    Let length of tower is h
    In \[\Delta \,ABD\]
                            \[\tan \,60{}^\circ =\frac{h}{4}\]                                               ?(i)
    In \[\Delta \,ABC\]
                            \[\tan \,30{}^\circ =\frac{h}{9}\]
                            \[\cot (90{}^\circ -30{}^\circ )=\frac{h}{9}\]
                            \[\cot \,60{}^\circ =\frac{h}{9}\]                                               ?(ii)
    Multiplying eq. (i) and (ii), we get
                            \[\tan \,60{}^\circ .\cot \,60{}^\circ =\frac{h}{4}\times \frac{h}{9}\]
                                        \[1=\frac{{{h}^{2}}}{36}\]
                                        \[h=6\,m\]        
    Note: In this question, it has not been specified whether two points from tower are taken in same or opposite side we have taken these points on the same side of tower.


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