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.`

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) .

AB is a vertical pole resting at the end A on the level ground. P is a point on the level ground such that AP = 3AB and C Is the midpoint of AB. If AC and CB subtend angles alpha and beta , respectively, at P, then the value of tan beta is

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.

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

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 .

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.

From the top and bottom of a cliff the angles of depression and elevation of the top of a pillar 60ft high are observed to be 30^@ and 60^@ respectively. Find the height of the cliff.

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.

A stone is dropped from the top of a vertical pillar. When the stone has fallen through a height x, another stone is dropped from height y below the top of the pillar. Both the stones touch the ground at the same time . Prove that the height of the pillar should (x+y)^(2)/(4x) .

From the top of a cliff, 150 metres high, the angles of depression of the top and bottom of a pillar are found to be 30^@ and 60^@ respectively, find the height of the pillar.