Explanation:

Let’s break this down:

- You’ve got a lighthouse, 45 m high. The ship’s out at sea. The angles of depression to the ship change from 30° to 45° as it moves.

- Picture two right triangles, both using the lighthouse as the vertical leg (45 m), but with their bases at different distances (let’s call them x and y).

- For the 30° angle:

tan(30°) = 45 / x

So, x = 45 / tan(30°) = 45 / (1/v3) = 45 * v3 ˜ 77.94 m

- For the 45° angle:

tan(45°) = 45 / y

So, y = 45 / 1 = 45 m

- The ship travels the difference:

Distance = x - y = 77.94 - 45 = 32.94 m

- Rounded to one decimal, that’s 32.9 m.

- Option 1: 32.9 m

- Option 2: 33.4 m

- Option 3: 36.9 m

- Option 4: 24.8 m

No need to overthink it. Here’s the real deal:

OPTION 1 is correct.