The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is :

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°,then PC (in m) is equal to :

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 the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be 30^o, then the distance (in m) of the foot of the tower from the point A is :

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot^–1 (3$$\sqrt 2 $$ ) and cosec^–1 (2$$\sqrt 2 $$ ) respectively, then the height of the tower (in metres) is :