If the angles of elevation of two towers from the middle point of the line joining their feet are $60^\circ$ and $30^\circ$ respectively,then the ratio of their heights 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

$A$ flag-staff of $5 \, m$ high stands on a building of $25 \, m$ high. An observer is at a height of $30 \, m$. The flag-staff and the building subtend equal angles at the observer. The distance of the observer from the top of the flag-staff is

$A$ 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

$A$ 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:

$A$ person observes the top of a tower from a point $A$ on the ground. The angle of elevation of the tower from this point is $60^{\circ}$. He moves $60 \ m$ in the direction perpendicular to the line joining $A$ and the base of the tower to reach point $C$. The angle of elevation of the tower from point $C$ is $45^{\circ}$. Then, the height of the tower (in metres) is