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 ... $m$.

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object, the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

$A$ balloon is observed simultaneously from three points $A, B$ and $C$ on a straight road directly under it. The angular elevation at $B$ is twice and at $C$ is thrice that of $A$. If the distance between $A$ and $B$ is $200$ metres and the distance between $B$ and $C$ is $100$ metres,then the height of the balloon is:

Two vertical poles of heights $20 \ m$ and $80 \ m$ stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other,from this horizontal plane is:

$A$ $20 \ m$ long tree is broken by the wind such that its top touches the ground at an angle of $30^\circ$. The height from the ground at which the tree is broken is:

Two pillars of equal height stand on either side of a roadway which is $60 \, m$ wide. At a point in the roadway between the pillars,the angles of elevation of the top of the pillars are $60^\circ$ and $30^\circ$. The height of the pillars is