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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