From a point $P$ on a level ground,the angle of elevation of the top of a tower is $30^{\circ}$. If the tower is $100 \ m$ high,the distance (in $m$) of point $P$ from the foot of the tower is:

Two towers of equal height stand on either side of a wide road which is $100 \, m$ wide. At a point on the road between the towers, the angles of elevation of the tops of the towers are $60^{\circ}$ and $30^{\circ}$. Find their heights in metres. (in $\sqrt{3}$)

$A$ $20 \, m$ high electric pole stands upright on the ground with the help of a steel wire attached to its top and fixed on the ground. If the steel wire makes an angle of $60^{\circ}$ with the horizontal ground,find the length of the steel wire (in $m$).

$A$ man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of $45^{\circ}$ with the man's eye when at a distance of $60 \ m$ from the tower. After $5 \ s$,the angle of depression becomes $30^{\circ}$. What is the approximate speed (in $km/hr$) of the boat,assuming that it is running in still water?

The angle of elevation of the top of an unfinished tower at a point distant $120 \ m$ from its base is $45^{\circ}$. If the elevation of the top at the same point is to be $60^{\circ}$,the tower must be raised to a height of:

The angle of elevation of a tower from a distance of $100 \ m$ from its foot is $30^{\circ}$. Then the height of the tower is (in $m$):