Q41 of 68 Page 9

From a light-house, the angles of depression of two ships on opposite sides of the light-house are 30° and 45°. If the height of the light-house is 100 m, find the distance between the ships, if the line joining them passes through the foot of the light-house.


Let the two ships be at C and D with angles of depression 45° and 30° from point A.


The height of the light house, AB = 100m


In the right Δ ABD, we have




⇒ BD = 100√3 …(i)


In right Δ ABC, we have




⇒ BC = 100m


Hence, the distance between the two ships = BC + BD


= 100 + 100√3


= 100(1 + √3)


= 100(1 + 1.732)


= 100(2.732)


= 273.2 m (approx.)


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