20. A tourist looks out from the crown of the Statue of Liberty, which is 250 ft tall. *

Question

The tourist sees a ship coming into the harbor and measures the angle of depression as 18 degrees. Find the distance from the base of the Statue of Liberty to the ship to the nearest foot.
237.8 ft
77.3 ft
81.2ft
769.4 ft

Answer 1

To solve this problem, we can use trigonometry.

Let's assume the distance from the base of the Statue of Liberty to the ship is x ft.

We have an angle of depression of 18 degrees from the tourist's viewpoint, and we want to find the distance x.

Using the tangent function, we can set up the following equation:

tan(18) = opposite/adjacent

Thus, tan(18) = 250/x

To find x, we can rearrange the equation as follows:

x = 250/tan(18)

Plugging this into a calculator, we find:

x ≈ 769.4 ft

Therefore, the distance from the base of the Statue of Liberty to the ship is approximately 769.4 ft.