A ship is 750 meters from a light house which is 50 meters tall. What is the angle of depression from the top of the lighthouse to the ship?

same as the angle from the horizon to the top of the lighthouse from the ship

tan T = 50/750
T = 3.81 degrees

make your sketch

angle at water --- Ø

tanØ = 50/750 = 1/15
Ø = appr 3.81°

which is also the angle of depression

To find the angle of depression from the top of the lighthouse to the ship, 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.

In this case, we have a right-angled triangle formed by the lighthouse, the ship, and the horizontal line. The height of the lighthouse is the opposite side of the triangle, and the distance from the lighthouse to the ship is the adjacent side. We can use the tangent function to determine the angle of depression.

The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. Therefore, we can calculate the angle of depression using the formula:

tan(angle) = opposite / adjacent

In this case, the height of the lighthouse is 50 meters and the distance from the lighthouse to the ship is 750 meters. Plugging these values into the formula, we get:

tan(angle) = 50 / 750

To find the angle itself, we can take the inverse tangent (arctan) of both sides:

angle = arctan(50 / 750)

Using a calculator or an online trigonometric calculator, we can find the arctan value of 50 / 750, which is approximately 3.805 degrees.

Therefore, the angle of depression from the top of the lighthouse to the ship is approximately 3.805 degrees.