from the top of a light house the angle of depression of a ship sailing towards it was found to be 30 degrees . after 10 seconds the angle of depresion changes to 60 degrees. assuming that the ship is sailing at uniform speed. find how much time it will take to reach the light house?

Answer 1

Locate points on the ocean:
Let the point at 30 degrees be A
Let the point at 60 degrees be B
Let the base of the lighthouse be point C
Let the height of the lighthouse be h

h/BC = tan 60 = √3
h/AC = tan 30 = 1/√3

√3 BC = 1/√3 AC
3BC = AC

That means AC = AB + BC
SO, 3BC = AB + BC
So, AB = 2BC

AB was traveled in 10 seconds.
So, BC will take only 5 seconds to cover.

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