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Q:

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) 173 m B) 200 m
C) 273 m D) 300 m

Answer:   C) 273 m



Explanation:

 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°=1√3=>AC=AB*√3=100√3m

 

 

 ABAD=tan45°=1=>AD=AB=100m

CD=(AC+AD)=(100√3+100)m=100(√3+1)=100*2.73=273m

Subject: Height and Distance
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