Question

Find the angle of depression from the top of a lighthouse 400 feet above water level to the water line of a ship 18,410 ft offshore? Round your answer to the nearest hundredth of a degree.

Answer 1

To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.

tan(angle) = opposite / adjacent

tan(angle) = 400 / 18,410

Now, we'll use the arctangent (inverse tangent) function to find the angle:

angle = arctan(400 / 18,410)

angle ≈ 1.25 degrees

The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.

Answer 2

The angle of depression from the top of a lighthouse 400 feet above water level to the water line of a ship 18,410 ft offshore can be calculated using trigonometry.

tan θ = opposite/adjacent

In this case, the opposite is the height of the lighthouse (400 ft) and the adjacent is the horizontal distance from the lighthouse to the ship (18,410 ft).

tan θ = 400/18,410

θ = arctan(400/18,410)

θ ≈ 1.24°

Therefore, the angle of depression from the top of the lighthouse to the water line of the ship is approximately 1.24°.