Question

The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is

A) 60 m B) 45 m C) 50 m D) 75 m

Answer 1

$\huge\star\red{{Answer}}$

∆ABE tan 30° = AB/EB

1/√3 = h/x

= = > x = √3 × h ......1)

tan 60° = BD/EB

√3 = h + 30 + 30 / x

= = > √3 = h + 60 / √3h

= = > 3h = h + 60

= = > 2h = 60

= = > h = 30m

Height from water surface = 30 + 30 = 60m