Question

From an airplane flying over the ocean, the angle of depression to a submarine lying under the surface if 24 degrees 10 minutes. At the same moment, the angle of depression from the airplane to a battleship is 17 degrees 30 minutes. The distance from the airplane to the battle ship is 5120 ft. Find the distance between the battleship and the submarine.

Answer 1

To find the distance between the battleship and the submarine, we can use trigonometry and the angles of depression. The values for the angles of depression and the distance from the airplane to the battleship are given. Solving the trigonometric equations will give us the distance between the battleship and the submarine.

Step-by-step explanation:

To find the distance between the battleship and the submarine, we can use trigonometry and the angles of depression. Let's denote the distance between the submarine and the battleship as x. From the airplane, the angle of depression to the submarine is 24 degrees 10 minutes, and to the battleship is 17 degrees 30 minutes. We can set up the following trigonometric equations:

tan(24° 10') = (25 + x) / x (since the submarine is 25 ft below the surface)

tan(17° 30') = (5120 + x) / x (since the battleship is 5120 ft away)

Solving these equations will give us the value of x, the distance between the battleship and the submarine.