Q. 273.7( 10 Votes )

From a point 100

Answer :

The figure for the question is


Let A be the point 100 m above lake and C be the helicopter and C' be the reflection of helicopter in water.


Given,


Angle of elevation of helicopter from point A, ∠CAQ = 30° [Let θ1]


Angle of depression of reflection from point A, ∠QAC' = 60° [Let θ2]


Also,


AB = PQ = 100 m …[1]


AQ = BP …[2]


CP = CP' [image distance is equal to object distance]


And let CQ = 'x'


CP = CQ + PQ = 100 + x


⇒ CP' = 100 + x …[3]


In ΔACQ



From [2]



⇒ BP = x√3 m …[4]


In ΔAQC'




[From [3]]


3x = x + 200


⇒ 2x = 200


⇒ x = 100 m


And


Height of helicopter above lake = CP = x + 100


= 100 + 100 = 200 m

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