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∘ and 45∘ respectively. If the lighthouse is 100 m high, the distance between the two ships is:
273 m
Let AB be the lighthouse and C and D be the positions of the ships.
Then, AB = 100 m, ∠ ACB=30∘ and ∠ ADB 45∘
ABAC=tan 30∘ 1√3⇒AC=AB×√3=100×√3mABAD=tan 45∘=1⇒AD=AB=100 mSo,CD=(AC+AD)=(100√3+100) =100(√3+1) =(100×2.73) =273 m