Q. 524.8( 23 Votes )

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by

Answer :

In the fig let B & C be two mile stones. And height of the aeroplane is AD



In ∆ABD


tan α =


tan α =


h = BD tan α ……………………(1)


In ∆ACD


tan β =


tan β =


CD = …………………(2)


On adding eqn (1) and (2)


BD + CD =

Now as B and C are milestones, the distance between them = 1
Therefore, BD + CD = 1


1 =


h =

Proved

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