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 $m$):

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:

An aeroplane flying at a height of $5000 \; m$ from the ground passes vertically above another aeroplane at an instant. At that instant,the angles of elevation of the two aeroplanes from the same point on the ground are $60^{\circ}$ and $45^{\circ}$ respectively. The vertical distance between the aeroplanes at that instant is:

The shadow of a tower standing on a level plane is found to be $50 \ m$ longer when the sun's altitude is $30^{\circ}$ than when it is $60^{\circ} .$ Find the height of the tower. (In $m$)

The angle of elevation of the top of an unfinished tower at a point $120 \ m$ from its base is $45^{\circ}.$ How much higher (in $m$) must the tower be raised so that its angle of elevation is $60^{\circ}$ at the same point?

$A$ tower stands at the end of a straight road. The angles of elevation of the top of the tower from two points on the road $500 \ m$ apart are $45^{\circ}$ and $60^{\circ},$ respectively. Find the height of the tower.