A man observes a tower AB of height h from a point P on the ground. He moves a distance ‘d’ towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance 3d/4 in the same direction and the angle of elevation is three times that at P. Then 36h²=

At the foot of a mountain the angle of elevation of a summit is found to be 45⁰. After ascending 1 km towards the mountain up, a slope of inclination 30⁰, the angle of elevation is found to be 60⁰. The height of the mountain is

From the foot of a tower 220 m high the angle of elevation of the top of a hill is 60⁰ and from the top of the tower the angle of depression of the top of the hill is 300. The height of the hill and the distance between them are

A pole of height h stands at one corner of a park in the shape of an equilateral triangle. If α is the angle which the pole subtends at the midpoint of the opposite side, the length of each side of the park is