Final answer:
The distance of the ship from the foot of the light tower is calculated using tangent function tan(6°) = 40/d, and it is approximately 380m when rounded to two significant figures.
Step-by-step explanation:
To calculate the distance of the ship from the foot of the light tower, given that the light tower is 40m above sea level and the angle of depression is 6 degrees, we can use trigonometry. The angle of depression is equal to the angle of elevation from the ship to the top of the tower, due to alternate interior angles created by a parallel line to the sea level and the line of sight from the tower. Since we have a right-angled triangle with the tower height as the opposite side and the angle of elevation as 6 degrees, we can use the tangent function.
Let d be the distance we want to find, which is the adjacent side of the triangle. We can write the following equation based on the tangent of the angle:
tan(6°) = opposite/adjacent = 40/d
Rearranging the equation, we get:
d = 40 / tan(6°)
Calculating this using a calculator and rounding to 2 significant figures:
d ≈ 380.52m, when rounding to 2 significant figures, d ≈ 380m.