A flagstaff stands on the top of a tower. At a point distant d from the base of the tower, the angles of elevation of the top of the flagstaff and that of the tower are ]3 and a respectively. Prove that the height of the flagstaff is = d (tanβ – tan α).

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the width of the river.[ Use = 1.732 ]

A 10 m high flagstaff stands on a tower. From a point on the level ground, the angles of elevation of the foot and top of the flagstaff are 30° and 60° respectively. Find the height of the tower.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angle of elevation of the bottom of the flagstaff is α and that of the top of the flagstaff is β. Prove that the height of the h tan a tower is .

From a point on the level ground, the angle of elevation of the top of a tower is 30°. On proceeding 30 m towards the tower the angle of elevation becomes 60°. Find the height of the tower.