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From an aero plane vertically above a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aero plane are observed to be α and β. Show that the height of the aero plane above the road is
Tan α tanβ/ tan α + tanβ
Ans: Let P Q be h
QB be x
Given : AB = 1 mile
QB = x
AQ = (1- x) mile in ?PAQ
Tan α PQ /AQ
Tan α = h/1 - x
1-x = h/Tan α .............1
In ΔPQB
Tan β = h/ x
x = h/Tanβ
Substitute for x in equation (1)
1 = h/Tanβ + h /Tanα
1/h = Tanβ + Tanα/TanβTanα
∴h = Tan α tanβ/ tan α + tanβ
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