• 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.

 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 $\Delta \,DBC,\frac{DC}{BC}=\tan \,\,30{}^\circ =\frac{1}{\sqrt{3}}$ $\Rightarrow$               $BC=\sqrt{3}\,\,DC=50\sqrt{3}$ $h=BC\sqrt{3}$ $=50\sqrt{3}\times \sqrt{3}=50\times 3$ $=150\,\,m$