At a distance $2h$ from the foot of a tower of height $h$,the tower and a pole at the top of the tower subtend equal angles. The height of the pole is:

The angle of elevation of a jet plane from a point $A$ on the ground is $60^{\circ}$. After a flight of $20 \, s$ at the speed of $432 \, km/h$, the angle of elevation changes to $30^{\circ}$. If the jet plane is flying at a constant height, then its height is ..... $m$. (in $\sqrt{3}$)

$A$ bird is sitting on the top of a vertical pole $20 \ m$ high and its angle of elevation from a point $O$ on the ground is $45^o$. It flies off horizontally straight away from the point $O$. After one second,the angle of elevation of the bird from $O$ is reduced to $30^o$. Then the speed (in $m/s$) of the bird is

For a man,the angle of elevation of the highest point of the temple situated east of him is $60^\circ$. On walking $240 \ m$ to the north,the angle of elevation is reduced to $30^\circ$. The height of the temple is:

$ABC$ is a triangular park with $AB = AC = 100 \text{ metres}$. $A$ vertical tower of height $h$ is situated at the mid-point $P$ of $BC$. If the angles of elevation of the top of the tower $Q$ at $A$ and $B$ are $\cot^{-1}(3\sqrt{2})$ and $\csc^{-1}(2\sqrt{2})$ respectively,then the height of the tower (in metres) is

The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is