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

From an aeroplane vertically above a straight horizontal plane, the an

1.	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
Answer» 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*