$A$ man whose eye level is $1.5 \ m$ above the ground observes the angle of elevation of a tower to be $60^\circ$. If the distance of the man from the tower is $10 \ m$,the height of the tower is:

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base to be $30^{\circ}$. After walking $120 \ m$ towards it on level ground, the angle of elevation is found to be $60^{\circ}$. Then the height of the object (in metres) is:

In a triangular park $PQR$,$PQ = PR = 200 \ m$. $A$ $TV$ tower stands at the mid-point $M$ of $QR$. If the angles of elevation of the top of the tower at $P, Q,$ and $R$ are $45^o, 30^o,$ and $30^o$ respectively,then the height of the tower (in $m$) is:

$A$ 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

An observer in a boat finds that the angle of elevation of the top of a tower standing on the top of a cliff is $60^\circ$ and that of the top of the cliff is $30^\circ$. If the height of the tower is $60 \ m$,then the height of the cliff is ... $m$.

$A$ vertical pole consists of two parts,the lower part being one third of the whole. At a point in the horizontal plane through the base of the pole and at a distance of $20 \, m$ from it,the upper part of the pole subtends an angle whose tangent is $\frac{1}{2}$. The possible heights of the pole are