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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:
276 metre
273 metre
270 metre
263 metre
Let AB be the lighthouse and C and D be the positions of the ships. AB = 100m,∠ACB=30°, ∠ADB=45° AB/AC=tan30=1/√3 =>AC=AB∗√3=100√3m AB/AD=tan45 =>AB=AD=100m CD=AC+AD =(100√3+100) =100(√3+1)=273m
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