Question

From the top of a building AB, 60 m high, the angles of depression of the top and bottom of a vertical lamp post CD are observed to be 30° and 60° respectively. Find
(i) the horizontal distance between AB and CD.
(ii) the height of the lamp post.
(iii) the difference between the heights of the building and the lamp post.

Answer 1

(i) the horizontal distance between AB and CD = 20√3 m

(ii) the height of the lamp post = CD = 40 m

(iii) the difference between the heights of the building and the lamp post = 20 m

Consider the figure while going through the following steps:

tan 60° = AB/BD

√3 = 60/BD

BD = EC = 60/√3

∴ BD = 20√3 m............(i)

tan 30° = AE/EC

tan 30° = AE/BD

1/√3 = AE/20√3

∴ AE = 20 m    

EB = AB - AE

= 60 - 20

EB = CD

∴ CD = 40 m .............(ii)

AB - CD = 60 - 40

AE = 20 m .............(iii)