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 $^{\circ}$)

Two cars are parked in the same direction of a tower. Observing from the top of the tower,their angles of depression are found to be $60^{\circ}$ and $30^{\circ}$. If the car nearer to the tower is $75\, m$ away from the tower,find the distance between these two cars (in $m$).

Watching from the top of an $80 \, m$ high hill,the angle of elevation of the top of a tower is $30^\circ$ and the angle of depression of the base of the tower is $45^\circ$. Find the height of the tower in $m$.

$A$ boat is sailing with constant speed towards a man sitting on a tree on the river bank. At some moment,the man measures the angle of depression of the boat as $30^{\circ}$. $10$ minutes later,this angle is measured as $60^{\circ}$. How much longer will the boat now take to reach the bank? (in $min$)

As observed from the top of a $510 \ m$ high tower,the angles of depression of two houses situated in the east and west of the tower are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the distance between the two houses (in $m$).

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