Question

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?

Answer 1

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`