Answer :

Untitled29.jpg


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.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses