Final answer:
The distance from the ship to the base of the cliff can be calculated using the tangent of the angle of elevation (25°) and the height of the cliff (30m). The tangent function relates the angle to the ratio of the opposite side over the adjacent side in a right triangle.
Step-by-step explanation:
The question involves finding the distance from a ship to the base of a cliff using trigonometry. The ship spots the top of a lighthouse on a 30m cliff at an angle of 25°. To solve this problem, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. Here, the opposite side is the height of the cliff (30m) and the adjacent side is the distance from the ship to the base of the cliff, which we are trying to find.
Using the formula:
tan(θ) = opposite / adjacent
We find:
tan(25°) = 30m / adjacent
Therefore, the adjacent side (distance from the ship to the base of the cliff) can be calculated as:
adjacent = 30m / tan(25°)
After calculating, we get the distance from the ship to the base of the cliff. This applies the concept of trigonometry commonly taught in high school mathematics.