Question

From an aeroplane vertically above a straight horizontal road the angle of depression of two consecutive kilometer stones on the opposite sides of aeroplane are found to be 30 and 60 degrees.Find the height of the aeroplane

Answer 1

let AB be the height of plane = h   [answer =866m]
tan 60 = √3
tan 60 = AB/BD
where BD is the distance btw the plane and 1st km stone
∴√3=h/BD   (equation 1)
BD=h/√3
tan30 =1/ √3
tan30=AB/BC(where BC is the distance btw the plane and the 2nd km stone
1/√3=h/BC(equation 2) [now equate these two equations ]