The union of the horizontal ray and the ray of vision forms the angle of elevation; then the object under observation is $\ldots \ldots \ldots . .$

'True' or 'False' and justify your answer.
If a man standing on a platform $3 \ m$ above the surface of a lake observes a cloud and its reflection in the lake,then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

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 $\ldots \ldots \ldots \ldots$

$A$ pole stands erect on the ground. $A$ wire tied to the top of the pole is affixed at a point on the ground. If the length of the wire is $7 \, m$ and the wire makes an angle of $30^{\circ}$ with the ground,find the height of the pole (in $m$).

$A$ ladder is leaning against a wall such that its upper end touches the wall at a height of $3 \, m$ and the ladder is inclined at an angle of $30^{\circ}$ with the ground. Find the length of the ladder in $m$.

$A$ ladder leans on a wall to reach the height of $3\, m$ on the wall. If the ladder makes an angle of $30^{\circ}$ with the ground,the length of the ladder is ........$m.$