Discussion
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 degree and 45 degree respectively. If the lighthouse is 100 m high, the distance between the two ships is
Answer: A
The ships lie on opposite sides, so the lighthouse foot is between them and the two horizontal distances add.
\[ d_{30} = \frac{100}{\tan 30^{\circ}} = 100\sqrt{3} = 173.2 \text{ m} \]
\[ d_{45} = \frac{100}{\tan 45^{\circ}} = 100 \text{ m} \]
\[ \text{distance apart} = 173.2 + 100 = 273.2 \approx 273 \text{ m} \]
Had the ships been on the same side the answer would be the difference, 73 m. Answering 173 m counts only the \( 30^{\circ} \) ship.
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