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From the top of a tower of height 75 m, a man sees two goats, both due west of him. If the angles of depression of the two goats are 10 degrees and 17 degrees, calculate the distance between them.

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The man sees two goat from the top of a tower that is 75 m high. The angle of depression of the two goats is 10 degrees and 17 degrees.

Use the fact that the tower and the ground are perpendicular to each other and a right triangle is formed by the tower, the ground and the line joining each of the goats and the man.

The distance of the goat seen at an angle of depression 17 degrees from the tower is 75*tan (90-17) = 245.31 m and the distance of the other goat is 75*tan(90-10) = 425.346. The distance between them is approximately 425 - 245 = 180 m.

The distance between the two goats is 180 m.

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