Question

Two ships are sailing on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships at 30 degree and 45 degree respectively. If the lighthouse is 100m high, determine the distance that separate the ships

Answer 1

Answer:

Explanation

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:

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–√+100)m=100(3–√+1)=100*2.73=273m