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:

+2 votes

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:

+1 vote

sin 30 = 1/2 and sin x = Perpendicular/Hypoteneous.

so,

Perpendicular =100m

Hypoteneous=100/sin30=100*2=200

Now, Base1=sqrt(sqr(200)-sqr(100))=173.32

Similarly

Hypoteneous2 = Perpendicular/Sin 45 = 100*1.414=141.4

Base2=sqrt(sqr(141.4)-sqr(100))=99.96

Distance=Base1+Base2=173.76+99.96=273 m apporx

**Answer: Distance = 273 m (approx)**

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