Determine the height of a mountain if the elevation of its top at an unknown distance from the base is `30^@` and at a distance 10 km further off from the mountain, along the same line, the angle of elevation is `15^@`. (Use tan `15^@ = 0.27`).

A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60^@ . From a point 20maway from this point on the same bank, the angle of elevation of the top of the tower is 30^@ (see fig.). Find the height of the tower and the width of the canal.

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

The angle of elevation of the top of a tower from a point A on the ground is 30^@ . On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60^@ . Find the height of the tower and distance of the tower from the point A.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on theopposite 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.

A man is moving away from a tower 41.6 m high at the rate of 2 m/sec. Find the rate at which the angle of elevation of the top of tower is changing, when he is at a distance of 30m from the foot of the tower. Assume that the eye level of the man is 1.6m from the ground.

From the top of a building 15 m high, the angle of elevation of the top of a tower is found to be 30^@ . From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the distance between the tower and the building.

The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^@ . At a point Y, 40 m vertically above X, the angle of elevation is 45^@ . Find the height of the tower PQ and the distance XQ.

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30^@ . Find the height of the tower.