Heights, Distances & Applications

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  1. 1.

    A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 60 degrees. When he moves 40 m away from the bank, the angle becomes 30 degrees. Find the width of the river.

  2. 2.

    Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

  3. 3.

    From a point on the ground, the angle of elevation of the top of a tower is alpha. On walking a distance d toward the tower, the angle becomes beta. The height of the tower is:

  4. 4.

    The angle of elevation of the top of a tower from two points at distances a and b from the base (on the same side) are complementary. The height of the tower is:

  5. 5.

    From the top of a 60 m tower, the angles of depression of the top and bottom of a building are 30 degrees and 60 degrees respectively. Find the height of the building.

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