# From an aeroplane vertically above a straight horizontal plane, the angle of depression of two consecutive kilo-meter stones on the opposite sides of the aeroplane are found to be ? and ?. Show that the height of the aeroplanes is

So from fig

we get tan α = h/x ⇒ x = h/tan α   ......   (i)

and tan β = h/(1-x)

⇒ 1 - h/tanβ = x  ............. (ii)

using i and ii we get

⇒ h/tan α = 1 - h/tanβ

⇒  h(tan α + tanβ)/tanαtanβ = 1

⇒ h =

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