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 =