Let AB is a building of height 60 m and CD is a light house of height h m. The angle of elevation and angle of depression of the top and bottom of a light house from top of building are 30° and 60° respectively.
∠CAE = 30° and ∠EAD = 60°
∠ADB = ∠EAD = 60° (Alternate angle)
Draw BD || AE
∴ ∠AEC = 90° (Corresponding angle)
∠ABD + ∠BDE = 90° + 90° = 180°
∴ AB || DE
So, ABDE is a rectangle.
DE = AB = 60 m
and CE = (h – 60)m
From right angled ∆AEC,
tan 30° = CE/AE
1/√3 = (h - 60)/BD [∵ AE = BD]
⇒ BD = √3(h – 60)m …..(i)
From right angled ∆ABD,
Put the value in equation (ii) from equation. (i),
√3(h – 60) = 20 √3
⇒ h – 60 = 20√3/√3 = 20
⇒ h = 20 + 60 = 80 m
Hence, height of light house = 80 m
(i) Difference in height between light house and building
= 80 – 60 = 20 m
(ii) Distance between light house and building
BD = 20√3 m
