Question

# 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 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

A
300 m
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B
273 m
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C
200 m
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D
173 m
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Solution

## The correct option is B 273 m Let, BD be the lighthouse and A and C be the positions of the ships. Then, BD=100m, ∠BAD=30∘, ∠BCD=45∘ tan30∘=BDBA⇒1√3=100BA⇒BA=100√3tan45∘=BDBC⇒1=100BC⇒BC=100 Distance between the two ships =AC=BA+BC=100√3+100=100(√3+1)=100(1.73+1)=100×2.73=273m

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