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Question:

When observed from the top of a tower, the angle of depression of two houses A and B in the eastern and western directions is 30° and 60° respectively. Then which house is nearer to the tower?

None of the above.

House B is nearer to the tower than house A.

House A and B are equidistant from the tower.

House A is nearer to the tower than house B.

Solution:

LetMNbe the tower of heighth.HousesAandBare at distancesxandyfrom tower respectively.tan30o=hx⟹xtan30o=h⟹x√3=h.. (1)tan60o=hy⟹√3y=h(2)From (1) and (2), we writex√3=√3y⟹x=3yThus, distance ofAfrom tower is3times the distance ofBfrom the tower.Hence, houseBis nearer to tower than houseA.