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. 273 m B. 300 m C. 200 m D. 173 m Answer Workspace Report Discuss Answer with explanation Answer: Option A Explanation Let BD be the lighthouse and A and C be the positions of the ships. Then, BD = 100 m, BAD = 30° , BCD = 45° tan30°=BDBA⇒1√3=100BA⇒BA=100√3tan30°=BDBA⇒13=100BA⇒BA=1003 tan45°=BDBC⇒1=100BC⇒BC=100tan45°=BDBC⇒1=100BC⇒BC=100 Distance between the two ships = AC = BA + BC =100√3+100=100(√3+1)=1003+100=100(3+1) = 100(1.73+1) = 100 × 2.73 = 273 m Workspace
BAD = 30° ,
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