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 α and β. Show that the height of the aeroplanes is

tan \alpha * tan \beta / tan \alpha + tan \beta

1
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2015-02-08T13:01:49+05:30

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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 = { \frac{tan \alpha tan \beta }{(tan \alpha + tan \beta )}

 PROVED
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