There is a lighthouse on top of a cliff. The light of the lighthouse is 200 feet above sea level. It can be seen on the deck of a ship that is 25 feet above sea level. If the angle of depression from the light of the lighthouse to the deck of the ship is 30 degrees, then how far from the cliff is the ship, to the nearest foot?
We can imagine the ship, the lighthouse, and the base of the cliff forming a right triangle. The angle of depression from the light of the lighthouse to the deck of the ship is 30 degrees, so the angle between the top of the lighthouse and the deck of the ship is 90 - 30 = 60 degrees.
We can use the tangent function to find the distance from the cliff to the ship.
Let x be the distance from the cliff to the ship.
tan(60°) = (200 - 25)/x
√3 = 175/x
x = 175/√3
x ≈ 100.87
Therefore, the ship is approximately 101 feet from the cliff. Answer: \boxed{101}.