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.
IN ∆ ACD
tan45° =ADDC
=> 1 = 150DC
=> DC = 150 m
in ∆ ABD,
tan30° = ADDB
=> 1√3=150DB
=> DB = 150√3
=> DB = 150√3 m
DB = DC + CD
=> 150√3 = 150 + CD
=> (150√3 - 150) = CD
=> 150(1.732 - 1) = CD
[ √3 = 1.732 ]
=> CD = 150×0.732
=> CD = 109.8 m