Q29 of 30 Page 1

As observed from the top of a 100m high light house from the sea - level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use 3 = 1.732]


Given:


• AB = 100m


• ∠ EAD = 30°


• ∠ EAC = 45°


To find: CD, i.e. the distance between the boats


In ∆ ABC,


∠ ACB = ∠ EAC = 45°


(∵ alternate angles over parallel lines are equal)


tan∠ACB = tan45° = 1

In ΔABC,



⇒ AB = BC = 100m


In ∆ ABD,


∠ ADB = ∠ EAD = 30°


(∵ alternate angles are equal)




⇒ BD = 100√3 m


So CD (distance between the boats) = BD – BC = 100(√3 – 1)m


= 73.2 m (apprx.)

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