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 $m$).

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 $m$).

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 $m$)

$A$ tree stands vertically on the bank of a river. The angle of elevation of the top of the tree from a point exactly opposite to the tree on the other bank of the river is $60^{\circ}$. The angle of elevation of the top of the tree from a point $40 \ m$ away from that point is $30^{\circ}$. Find the width of the river and the height of the tree.

An observer $1.5\, m$ tall is $28.5\, m$ away from a tower. The angle of elevation of the top of the tower from his eyes is $45^\circ$. Then the height of the tower is ............ $m$.

Observing an object from the point of observation,if one gets the angle of depression,then the object under observation is.........