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Two ships are sailing in the sea on opposite sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships to be 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:
- 173 m
- 200 m
- 273 m
- 300 m
Correct answer: 273 m
Solution
For the ship at 30°, distance from the lighthouse base is 100/tan 30° = 100√3 m. For the ship at 45°, distance is 100/tan 45° = 100 m. Since the ships are on opposite sides, total distance = 100√3 + 100 ≈ 273 m.
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