Question

You are at the top of a lighthouse that is 550ft tall. You look down towards the ocean and see a dolphin. The angle of depression is 58. How far is the dolphin from the shore?

Answer 1

The question involves trigonometry to calculate the horizontal distance from the top of a 550ft tall lighthouse, with a 58-degree angle of depression, to a dolphin. The tangent function is used to relate the height of the lighthouse to the distance, by setting up a right-angled triangle and solving for the adjacent side.

Step-by-step explanation:

The question refers to determining the horizontal distance from the lighthouse to the dolphin using trigonometric principles, specifically the concept of the angle of depression. To find this distance, we assume a right-angled triangle where the height of the lighthouse and the distance to the dolphin form the opposite and adjacent sides respectively. The angle of depression corresponds to the angle of elevation from the dolphin to the top of the lighthouse, given that these angles are alternate interior angles formed by parallel lines.

First, convert the angle of depression to the angle of elevation, which is also 58 degrees. Now, using the height of the lighthouse which is 550 feet, we apply the tangent function which relates the opposite side (height of the lighthouse) to the adjacent side (distance from the shore).

Let the distance from the shore to the dolphin be x.

Tan(58 degrees) = 550 / x

Solving for x gives:

x = 550 / tan(58 degrees)

Calculate this using a calculator to get the distance in feet, which can then be converted to other units if necessary.