The angles of depression of two cars parked in the same direction of a $50\, m$ high tower are found to be $30^{\circ}$ and $60^{\circ}$. Find the distance between these two cars. (in $, m$)

The height of a tower is $30 \ m$. Find the length of the shadow of the tower,when the angle of elevation of the sun is $45^\circ$. (in $m$)

Watching from the top of a building $40 \, m$ high,the angle of depression of a moving car increases from $30^{\circ}$ to $45^{\circ}$ in some interval of time. Find the distance covered by the car in that interval of time. (in $m$)

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 $\ldots \ldots \ldots \ldots$

As observed from the top of a lighthouse,the angles of depression of two ships $P$ and $Q$ anchored in the sea on the same side are found to be $35^{\circ}$ and $50^{\circ}$ respectively. Then,from the lighthouse:

As observed from the top of a tower $30 \, m$ high,the angle of depression of a stone on the ground is found to be $45^{\circ}$. Find the distance between the stone and the tower (in $m$).