Two scuba divers are 20m apart below the surface of the water. They both spot a shark that is below them. The angle of depression from diver 1 to the shark is 47° and the angle of depression from diver 2 to the shark is 40°. How far are each of the divers from the shark?
Let's call the distance between diver 1 and the shark x and the distance between diver 2 and the shark y.
In a right triangle formed by diver 1, diver 2, and the shark, the tangent of the angle of depression from diver 1 to the shark is equal to x/20.
Therefore, tan(47°) = x/20.
Similarly, in the same right triangle, the tangent of the angle of depression from diver 2 to the shark is equal to y/20.
Thus, tan(40°) = y/20.
Solving these equations, we find that x = 20 * tan(47°) and y = 20 * tan(40°).
Using a calculator, we get x ≈ 23.45m and y ≈ 16.84m.
Thus, diver 1 is approximately 23.45m away from the shark, and diver 2 is approximately 16.84m away from the shark.