On walking for search of a ball $x$ metres on a hill making an angle of $30^{\circ}$ with the ground,one can reach a height of $y$ metres from the ground. Then $\ldots \ldots \ldots . . .$

The angle of depression of the top of a building from the top of a tower is $45^{\circ}$ and that of the base of the building from the top of the tower is $60^{\circ}$. If the height of the building is $7 \, m$,find the height of the tower.

The angle of elevation of the top of a vertical tower from a point on the ground is $60^{\circ}$. From another point $10 \, m$ vertically above the first,its angle of elevation is $45^{\circ}$. Find the height of the tower.

The angle of elevation of the top of a tower from two points at distances $s$ and $t$ from its foot are complementary. Prove that the height of the tower is $\sqrt{s t}$.

In $\Delta ABC$,$\angle B$ is a right angle. If $AC = 20$ and $BC = 10$,then $m\angle ACB = \ldots$ (in $^{\circ}$)

When the angle of elevation of the sun is $30^{\circ}$,the length of the shadow of a tower is $90\, m$. Find the height of the tower. (in $m$)