A vertical piller of height h cm stands on the plane ground. At a fixed point on the plane ground the height of the top of the piller and that of a point x cm below the top subtent angles `60^(@)` and `30^(@)` respectively. Prove that `x =(2h)/(3)`.

A vertical pillar of height h cm stands on the plane ground. At a fixed point on the plane ground the height of the top of the pillar and that of a point x cm below the top subtend angles 60^@ and 30^@ respectively. Prove that x=(2h)/3.

Two poles of heights 6m and 11m stand on a plane ground. If the distance between the feet of the poles is 12m find the distance between their tops.

Aright circular cylindrical tower with height 'h' and radius 'r', stands on the ground. Let 'p' be a point in the horizontal plane ground and ABC be the semi-circular edge of the top ofthe tower such that B is the point in it nearest top. The angles of elevation of the points A and B are 45^(@) and 60^(@) respectively. Show that h/r=(sqrt3(1+sqrt3))/2 .

The angles of elevation of the bottom and the top of the tower fixed at the top of a 20m high building, from a point on the ground are 45^@ and 60^@ respectively. The height of the tower is

Two poles of the height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12, the distance between their tops is____

From the point on the top of a palace of 60 metres height, it is observed that the angle of depression of the tip and the foot of a tower are 30^@ and 60^@ respectively. Find the height of the tower.

At a distance 2h m from the foot of a tower of height h m the top of the tower and a pole at the top of the tower subtend equal angles. Prove that the height of the pole should be (5h)/(3) m.

From a point on the roof of five-storied building the angle of elevation of the top of a monument and that of angle of depression of the foot of the monument are 60^(@) and 30^(@) respectively. If the height of the building is 16 metres, calculate the height of the monument and the distance of the building from the monument.

Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet wide. From a point between them on the road, the angles of elevation of the top of the poles are 60^(@) and 30^(@) respectively. Find the height of the poles and the distances of the point from the poles.

A statue stands on the top of a 2m tall pedestal. From a point on the ground, the angle ofelevation of the top of the statue is 60^(@) and from the same point, the angle of elevation of the top of the pedestal is 45^(@) . Find the height of the statue.