question_answer

From the top of a \[7m\] high building, the angle of elevation of the top of a tower is \[60{}^\circ \] and the angle of depression of its foot is \[45{}^\circ \]. Find the height of the tower.

Answer:

Let C be top of a \[7m\] building CD and AB be tower. From C, draw \[CE\bot AB\], so EBDC is a rectangle.

From \[\Delta \text{ }CBD,\text{ }tan\text{ }45{}^\circ =\frac{CD}{BD}\]

or                       \[BD=CD=7\,m\]

From \[\Delta \,AEC\]

\[\frac{AE}{EC}=\tan \,\,60{}^\circ \]

\[\Rightarrow \]               \[AE=EC\,\,\tan \,\,60=7\sqrt{3}\]

\[[\because \,EC=BD]\]

Height of tower is \[AB=AE+EB=AE+DC\]

\[=7\sqrt{3}+7\]

\[7\left( \sqrt{3}+1 \right)m\]