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

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: Correct Answer 273 m

 Let AB be the lighthouse and C and D be the positions of the ships.

 

 

Then, AB = 100m, ∠ACB = 30°and∠ADB =45°

 

ABAC=tan30°=13=>AC=AB*3=1003m

 

 

 ABAD=tan45°=1=>AD=AB=100m

CD=(AC+AD)=1003+100m=1003+1=100*2.73=273m

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