Find the angle of depression from the top of
a lighthouse 191 feet above the water level to
the water line of a ship 4 miles offshore.
tanθ = 191/(4*5280)
note that for small angles (in radians)
tanθ ≈ θ
To find the angle of depression from the top of a lighthouse to the water line of a ship, where the lighthouse is 191 feet above the water level and the ship is 4 miles offshore, we can use trigonometry.
First, let's draw a diagram to visualize the situation. Consider the lighthouse as point A and the ship as point B. We have a right triangle with the lighthouse as the right angle, the height of the lighthouse as the opposite side (191 feet), and the distance from the lighthouse to the ship as the adjacent side (4 miles or 21120 feet). We are looking for the angle of depression, which is the angle formed between the line of sight from the top of the lighthouse to the water line of the ship and the horizontal line.
To find the angle of depression, we will use the tangent function, which is defined as the opposite side divided by the adjacent side.
tan(angle) = opposite / adjacent
In this case, the opposite side is the height of the lighthouse (191 feet), and the adjacent side is the distance from the lighthouse to the ship (21120 feet).
tan(angle) = 191 feet / 21120 feet
Now, we can solve for the angle by taking the arctan of both sides:
angle = arctan(191 feet / 21120 feet)
Using a calculator, we find that the angle is approximately 5.19 degrees.
Therefore, the angle of depression from the top of the lighthouse to the water line of the ship is approximately 5.19 degrees.