From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by

Question

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be &#x3B1; and &#x3B2;. Show that the height in miles of aeroplane above the road is given by

Philoid · Accepted Answer

In the fig let B & C be two mile stones. And height of the aeroplane is AD

In ∆ABD

tan α =

h = BD tan α ……………………(1)

In ∆ACD

tan β =

CD = …………………(2)

On adding eqn (1) and (2)

BD + CD =

1 =

h = Proved