Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is $\ldots \ldots \ldots . . .$

From the top of a building $h \ m$ high,the angle of elevation of the top of a pole is found to be $\alpha$,while the angle of depression of the base of the pole is found to be $\beta$. Prove that the height of the pole is $h(1 + \tan \alpha \cdot \cot \beta) \ m$.

When observed from the top of a tower,the angles of depression of two houses $A$ and $B$ in the Eastern and Western directions are $30^{\circ}$ and $60^{\circ}$ respectively. Then........

Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is.........

Two poles are $x$ metres apart and the height of one is double than that of the other. If from the midpoint of the line joining their feet,an observer finds the angle of elevation of their tops to be complementary,then the height of the shorter pole is $\ldots \ldots \ldots \ldots$

Write 'True' or 'False' and justify your answer.
The value of $\tan \theta$ (where $\theta < 90^{\circ}$) increases as $\theta$ increases.