Question

From the top of a lighthouse, the angle of depression to a buoy is 25 degrees. If the top of the lighthouse is 150 feet above sea level, find the distance from the buoy to the foot of the lighthouse.

A. 150 feet
B. 300 feet
C. 600 feet
D. 900 feet

Answer 1

To calculate the distance from the buoy to the foot of the lighthouse, the tangent of the 25-degree angle of depression is used, resulting in an approximate distance of 300 feet, which means option B is correct.

Step-by-step explanation:

To find the distance from the buoy to the foot of the lighthouse using the angle of depression, we can use the concept of right triangles and trigonometry. The angle of depression is equal to the angle of elevation from the foot of the lighthouse to the line of sight to the buoy. To solve the problem, we'll apply the tangent function which is the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the lighthouse and the adjacent side is the distance from the buoy to the foot of the lighthouse that we want to find.

Let's denote the distance as 'd'. Using the tangent of the angle of depression (25 degrees), we have:

tan(25 degrees) = opposite/adjacent = 150 feet / d

Solving for 'd', we get:

d = 150 feet / tan(25 degrees)

When we calculate this, we find that 'd' is approximately 300 feet. Hence, the correct answer is B. 300 feet.