From the top of a 230-ft lighthouse, the angle of depression to a ship in the ocean is 28°. How far is the ship from the base of the lighthouse? (Round your answer to the nearest foot.)
Solution:
To solve this problem, we can use trigonometry. The angle of depression is the angle formed between the line of sight from the top of the lighthouse to the ship and the horizontal line.
Let's assume that the distance from the base of the lighthouse to the ship is x feet.
Using the tangent function, we can set up the following equation:
tan(28°) = 230 / x
To find x, we can rearrange the equation:
x = 230 / tan(28°)
Using a calculator, we can evaluate the tangent of 28°:
tan(28°) ≈ 0.5317
Now, we can substitute this value into the equation:
x = 230 / 0.5317
x ≈ 432.33
Therefore, the ship is approximately 432 feet from the base of the lighthouse.