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Math Asked by a SnapAndSolve user · about 1 hour ago

Select the correct answer. An observatory is 150 feet high. When a person is standing in the observatory...

Select the correct answer.
An observatory is 150 feet high. When a person is standing in the observatory looking at an island, the angle of depression is 25°. What is the approximate horizontal distance from the observatory to the island?
355 feet
166 feet
70 feet
322 feet

Answer

To find the horizontal distance, we use the tangent of the angle of depression, which is equal to the opposite side (height of the observatory) over the adjacent side (horizontal distance).

tan(25°) = 150 / distance

Solving for distance:

distance = 150 / tan(25°)

Using a calculator, tan(25°) ≈ 0.4663.

distance ≈ 150 / 0.4663 ≈ 321.6 feet

The closest answer is 322 feet.

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