As observed from a hill $340 \ m$ high,the angles of depression of two houses situated to the east and west of the hill are found to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the distance between the two houses. (in $m$)

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 $\ldots \ldots \ldots \, m$.

The angle of depression of a car parked on the road as observed from the top of a building is $60^{\circ}$. The angle of depression of that car from a window $14.6 \, m$ below the top is $45^{\circ}$. Find the distance between the car and the building (in $m$).

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.

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 $\ldots \ldots \ldots \ldots$

Observing from the top of a tower,the angle of depression of an object $30 \ m$ away from the base of the tower is found to be $45^\circ$. Find the height of the tower (in $m$).