• # 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.

 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.