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Question

As observed from top of a 150 m tall light house, the angles of depression of two ships approaching it are 30 and 45. If one ship is directly behind the other, find the distance between the two ships.

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Solution

IN ∆ ACD

tan45° =ADDC

=> 1 = 150DC

=> DC = 150 m

in ∆ ABD,

tan30° = ADDB

=> 13=150DB

=> DB = 1503

=> DB = 1503 m


DB = DC + CD

=> 1503 = 150 + CD

=> (1503 - 150) = CD

=> 150(1.732 - 1) = CD
[ 3 = 1.732 ]

=> CD = 150×0.732

=> CD = 109.8 m


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