Answer:
1678 feet
Step-by-step 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:
[tex]d=2000 ft[/tex] the vertical distance covered by the submarine
[tex]h[/tex] = the horizontal distance travelled by the submarine
[tex]\theta=40^{\circ}[/tex] 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:
[tex]tan \theta = \frac{h}{d}[/tex]
Since h is the side opposite to the angle and d is the side adjacent to the angle.
The equation can be rewritten as
[tex]h=d tan \theta[/tex]
And by substituting the values, we find:
[tex]h=(2000)(tan 40^{\circ})=1678 ft[/tex]
