Question

From the top of a 300-ft lighthouse, the angle of depression to a ship in the ocean is 25°. How far is the ship from the base of the lighthouse?

Answer 1

The ship is approximately 671.21 feet away from the base of the lighthouse.

Step-by-step explanation:

To find the distance from the base of the lighthouse to the ship, we can use trigonometry.

Let x be the distance from the base of the lighthouse to the ship.

We have the opposite side (height of the lighthouse) and the angle of depression.

Tan(25°) = 300ft / x

Therefore, x = 300ft / tan(25°).

Using a calculator, x ≈ 671.21ft.

Hence, the ship is approximately 671.21 feet away from the base of the lighthouse.

Answer 2

Refer to the diagram shown below.

Let d = distance of the ship from the base of the lighthouse.

By definition,
tan(25°) = 300/d
d = 300/tan(25°) = 643.35 ft

Answer: The distance is 643.4 ft (nearest tenth)