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 \[\Delta \,DBC,\frac{DC}{BC}=\tan \,\,30{}^\circ =\frac{1}{\sqrt{3}}\]

\[\Rightarrow \]               \[BC=\sqrt{3}\,\,DC=50\sqrt{3}\]

\[h=BC\sqrt{3}\]

\[=50\sqrt{3}\times \sqrt{3}=50\times 3\]

\[=150\,\,m\]