Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If $$\angle $$BPC = $$\beta $$, then tan$$\beta $$ is equal to:

The angle of elevation of the top of a vertical tower from a point A, due east of it is 45^o. The angle of elevation of the top of the same tower from a point B, due south of A is 30^o. If the distance between A and B is $$54\sqrt 2 \,m,$$ then the height of the tower (in metres), is :

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30^o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60^o. Then the time taken (in minutes) by him, from B to reach the pillar, is :

If the angles of elevation of the top of a tower from three collinear points $$A, B$$ and $$C,$$ on a line leading to the foot of the tower, are $${30^ \circ }$$, $${45^ \circ }$$ and $${60^ \circ }$$ respectively, then the ratio, $$AB:BC,$$ is :