Question

In Fig. from the top of a building AB, 60 metres 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.

Answer 1

Given AB is the building and CD is the vertical lamp post. Then, DE is the horizontal distance between AB and CD. Let CD = h metres. Then

∠EDB = 30° and ∠ACB = 60°, AE = CD = h metres and EB = (60 – h) m

Now, in ∆ABC

(i) Horizontal distance between AB and CD = 20√3 m = 20 × 1.732 = 34.64 m
(ii) The height of lamp post = 40 m