In the above figure, let AB be the building such that AB = 60 m. Join A and X. The angles of depression are ∠CAX = 30° and ∠DAX = 60°. Let CD be the lamp post. Join C,D and B,D and C,E. Since AX is parallel to DB, we must have ∠XAC = ∠ACE = 30° and ∠XAD = ∠ADB = 60°. We get two right-angled triangles ∆ABD and ∆CAE. We use trigonometric angle tan in both the triangles with AB as height and DB as base (for ∆ABD) and AE as height and CE as base(for ∆CAE).

We have to find, (i)BD, (ii)CD, and (iii) AB-CD.

From ∆ABD,

or,

DB = CE.

From ∆ACE,

or,

or,

Hence,

And, the difference between the heights of the building and the lamp post is,

Thus our solutions are,

(i) The horizontal distance between AB and CD = 34.64 m.

(ii) The height of the lamp post = 40 m.

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