Q. 205.0( 4 Votes )

The angle of depression from the top of a tower of a point A on the ground is 30°. On moving a distance of 20 meters from the point A towards the foot of the tower to a point B, the angle of elevation of the top of the tower from the point B is 60°. Find the height of the tower and its distance from the point A.

Answer :


Let DC be the tower. Given that the angle of depression of the point A on the ground from the top of the tower DC is 30°. Join C and A. Now draw a line DE parallel to CA. Also join A and D. Then, EDA = 30°. We get a right-angled triangle ACD with right angle at C and DAC = 30°. If we move 20 m from A to B towards the foot of the tower C, then the angle of depression changes to 60°. Then, AB = 20 m. Join D and B. Then we get a right-angled triangle ∆DCB with right angle at C.

We are to find the height of the tower that is DC and its distance from A, that is, AC.

Let DC = x. In ∆DCB,


In ∆ADC,




The height of the tower = DC = x = 17.32m.

We have, BC = x/√3 = 10m. So, a distance of A from the tower = AC = 20 + 10 = 30m.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Heights and Distances33 mins
Quiz | Imp. Qs. on Heights and Distances37 mins
NCERT | Basics of Heights and Distances37 mins
Idioms and Phrases43 mins
Goprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and Nomenclature52 mins
Goprep Genius Quiz | Direction and Distance58 mins
Light and it's Reflection58 mins
Tropic and Nastic Movements32 mins
Learn to Make Your Own Acid Rain and pH Paper at Home!27 mins
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
view all courses