21 Find the angle of depression from the top of a lighthouse 400 feet above water level to the water line of a ship 3.5 miles offshore? Round your answer to the nearest hundredth of a degree.

To find the angle of depression, we can use trigonometry. The height of the lighthouse is 400 feet and the distance to the ship is 3.5 miles, which is equivalent to 3.5 x 5280 = 18480 feet. We can use the tangent function, where the angle (θ) can be found using the formula: tan(θ) = opposite / adjacent = 400 / 18480. Now calculating θ gives us: θ = arctan(400 / 18480) ≈ 1.26 degrees. So, the angle of depression is approximately 1.26 degrees when rounded to the nearest hundredth. The concept of angle of depression is not just limited to lighthouses; it's also crucial in fields like navigation and architecture. For instance, when pilots approach a runway, they must calculate angles of descent for a safe landing, which helps ensure they land at the correct angle for the runway. This practice is essential to avoid accidents and ensure smooth transitions from the air to the ground. Another fun fact is that angle calculations in real life often involve multiple tools and methods, but one common mistake is confusing the angle of depression with the angle of elevation. Remember, the angle of elevation goes up from your line of sight (like looking up at a tall building), while the angle of depression goes down (looking down at something below you, like a ship from a lighthouse!). Keeping this distinction clear can really help you ace any kind of trigonometry problem involving heights and distances!