$A$ pole stands vertically inside a triangular park $\Delta ABC$. Let the angle of elevation of the top of the pole from each corner of the park be $\frac{\pi}{3}$. If the radius of the circumcircle of $\Delta ABC$ is $2$,then the height of the pole is equal to:

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:

The angle of elevation of the top of a tower from the top of a house is $60^\circ$ and the angle of depression of its base is $30^\circ$. If the horizontal distance between the house and the tower is $12 \ m$,then the height of the tower 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:

Two vertical poles are $150 \ m$ apart and the height of one is three times that of the other. If from the middle point of the line joining their feet,an observer finds the angles of elevation of their tops to be complementary,then the height of the shorter pole (in meters) is

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be $45^o$ from a point $A$ on the plane. Let $B$ be a point $30 \, m$ vertically above the point $A$. If the angle of elevation of the top of the tower from $B$ is $30^o$,then the distance (in $m$) of the foot of the tower from the point $A$ is: