Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45″, respectively. If the lighthouse is 100 m high, the distance between the two ships is?
- 300 m
- 173 m
- 273 m
- None of these
Explanation
Let's denote the distance from the lighthouse to the ship observing at 30° as x and to the ship observing at 45° as y.
For the ship observing at 30°:
tan(30°) = 100 / x
x = 100 / tan(30°)
x = 100 / (1/√3)
x = 100√3
x ≈ 173 m
For the ship observing at 45°:
tan(45°) = 100 / y
y = 100 / tan(45°)
y = 100 / 1
y = 100 m
The distance between the two ships is x + y ≈ 173 + 100 ≈ 273 m.
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