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A submarine is getting ready to dive below the surface of the water at an angle of depression of 40 degrees. It will be at a depth of 2000 feet when it is finished with its dive. What will be the horizontal distance traveled when it's finished it's dive?

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Answer:

1678 feet

Explanation:

In this problem, the submarine travels at an angle of depression of 40 degrees, and it reaches a depth of 2000 feet when it is finished with the dive.

Therefore, we can call:


d=2000 ft the vertical distance covered by the submarine


h = the horizontal distance travelled by the submarine


\theta=40^(\circ) is the angle of depression

By analzying the situation, we notice that d and h represent the two sides of a right triangle.

Therefore, we can write the following equation:


tan \theta = (h)/(d)

Since h is the side opposite to the angle and d is the side adjacent to the angle.

The equation can be rewritten as


h=d tan \theta

And by substituting the values, we find:


h=(2000)(tan 40^(\circ))=1678 ft

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