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1. The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill?

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Let's denote the height of the hill as hh meters. We can set up a right triangle to represent the situation. From the given information: The angle of elevation of the top of the hill from the foot of the tower is 60 degrees. The angle of elevation of the top of the tower from the foot of the hill is...
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Let's denote the height of the hill as hh meters. We can set up a right triangle to represent the situation.

From the given information:

  1. The angle of elevation of the top of the hill from the foot of the tower is 60 degrees.
  2. The angle of elevation of the top of the tower from the foot of the hill is 30 degrees.
  3. The height of the tower is 50 meters.

In the right triangle formed by the hill, tower, and the ground, the height of the hill, the height of the tower, and the distance from the foot of the tower to the foot of the hill form the sides of the triangle.

Using trigonometric ratios, we can set up equations based on the given angles and the known side lengths:

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