# From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by

In the fig let B & C be two mile stones. And height of the aeroplane is AD

In ∆ABD

tan α =

tan α =

h = BD tan α ……………………(1)

In ∆ACD

tan β =

tan β =

CD = …………………(2)

On adding eqn (1) and (2)

BD + CD =

Now as B and C are milestones, the distance between them = 1
Therefore, BD + CD = 1

1 =

h =

Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trick to learn all Trigonometric Formulae28 mins
Champ Quiz | Trigger on Trigonometry47 mins
Fundas of Trigonometry50 mins
NCERT | Trigonometric Identities52 mins
Champ Quiz | Trigonometry Important Questions33 mins
Champ Quiz | NTSE Trigonometry50 mins
Testing the T- Ratios of Specified Angles57 mins
Foundation | Cracking Previous Year IMO QuestionsFREE Class
Basic Concept of Trigonometry43 mins
NCERT | Imp. Qs. on Trigonometry42 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