Q. 145.0( 8 Votes )

Two pillars of equal height stand on either side of a road, which is 100 m wide. The angles of elevation of the top of the pillars have measure 60 and 30 at a point on the road between the pillars. Find the position of the point from the nearest end of a pillars and the height of pillars.

Answer :

Let AB and DE be two pillars of equal height.


AB = DE



The angle of elevation of A and E from C are respectively 60⁰ and 30⁰ respectively.


ACB = 60⁰, EDC = 30⁰ and BD = 100 m


Let BC = x


CD = BD – BC = 100 – BC = (100 – x)


In ∆ABC,




… …. (1)


In ∆EDC,



(AB = DE)


100 – x = √3AB



100√3 – AB = 3AB


4AB = 100√3


AB = 25√3


= 25 × 1.73


= 43.25 m


The height of the pillar is 43.25 m.


From equation(1),




= 25


The distance of the point from the nearest end of the pillars is 25 m and the height of each pillar is 43.25 m.


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 DistancesHeights and DistancesHeights and Distances33 mins
Quiz | Imp. Qs. on Heights and DistancesQuiz | Imp. Qs. on Heights and DistancesQuiz | Imp. Qs. on Heights and Distances37 mins
NCERT | Basics of Heights and DistancesNCERT | Basics of Heights and DistancesNCERT | Basics of Heights and Distances37 mins
Idioms and PhrasesIdioms and PhrasesIdioms and Phrases43 mins
Goprep Genius Quiz  | Analogy and ClassificationGoprep Genius Quiz  | Analogy and ClassificationGoprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and NomenclatureAcid - Types and NomenclatureAcid - Types and Nomenclature52 mins
Puzzles and RiddlesPuzzles and RiddlesPuzzles and Riddles44 mins
Combination and Decomposition ReactionsCombination and Decomposition ReactionsCombination and Decomposition Reactions59 mins
Surface Area and VolumesSurface Area and VolumesSurface Area and Volumes43 mins
Resources and DevelopmentResources and DevelopmentResources and Development34 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
caricature
view all courses
RELATED QUESTIONS :