The angle of elevation of the top of the tower from a point $x \, m$ away from the tower is $30^{\circ}$. Then the height of the tower is $\ldots \ldots \ldots \, m$.

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 $^{\circ}$)

The angle of elevation of the top of a pole from a point $x \, m$ away from the base of the pole is $60^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

Watching from a point on the ground $20 \, m$ away from the base of an erect pole,the angle of elevation of the top of the pole is found to be $45^{\circ}$. Then,the height of the pole is $\ldots \ldots \ldots \, m$.

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 $\Delta ABC$,$m \angle B = 90^{\circ}$. If $m \angle C = \theta$,then $\tan \theta = \dots$