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 $m$).

The height of a lighthouse is $100\, m$. Two boats are anchored in the opposite directions from the lighthouse. The angle of depression of each boat from the top of the lighthouse is found to be $30^\circ$. Find the distance between these two boats (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.

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:

$A$ straight highway leads to the foot of a tower. $A$ man standing at the top of the tower observes a car at an angle of depression of $30^{\circ}$,which is approaching the foot of the tower with a uniform speed. Six seconds later,the angle of depression of the car is found to be $60^{\circ}$. Find the time taken by the car to reach the foot of the tower from this point (in $seconds$).

$A$ circus artist is climbing a $20\, m$ long rope,which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole,if the angle made by the rope with the ground level is $30^{\circ}$ (see figure). (in $m$)