An erect tree is $300\, m$ away from a hill. If the height of the hill is $300\, m$,find the angle of depression of the base of the tree from the top of the hill. (in $^{\circ}$)

In $\Delta ABC$,$m\angle B = 90^\circ$,$m\angle C = 30^\circ$ and $AC = 30 \text{ cm}$,then $AB = \ldots \text{ cm}$.

The shadow of a tower standing on a level plane is found to be $50 \, m$ longer when the Sun's elevation is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower (in $m$).

$A$ tower stands vertically on the ground. The angle of elevation of the top of the tower from a point $100 \, m$ away from the base of the tower is $60^\circ$. The height of the tower is $\ldots \ldots \ldots \ldots \, m$.

Write 'True' or 'False' and justify your answer.
If the length of the shadow of a tower is increasing,then the angle of elevation of the sun is also increasing.

$A$ ladder leans against a wall. It makes an angle of $45^{\circ}$ with the ground and reaches a height of $10 \, m$ on the wall. Find the length of the ladder and the distance between the lower end of the ladder and the base of the wall.