Q. 684.0( 9 Votes )

The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30° respectively. If the ships are 200 m apart, find the height of the light house.

Answer :

In the fig let AB is the light house of height h (m)


In ∆ABC



tan 30° =


=


√3h = 200 + x ………………….(1)


In ∆ABD


tan 45° =


1 =


h = x ………………(2)


From eqn (1) and (2) we get


√3h = 200 + h


h(√3 + 1) = 200


h =


On multiplying and dividing by √3-1, we get


h =


h = 273.2m


Therefore height of the light house is 273.2m


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
Champ Quiz | Trigonometry Important Questions33 mins
NCERT | Trigonometric Identities52 mins
Champ Quiz | NTSE Trigonometry50 mins
Testing the T- Ratios of Specified Angles57 mins
Foundation | Cracking Previous Year IMO QuestionsFREE Class
NCERT | Imp. Qs. on Trigonometry42 mins
Quiz | Trail of Mixed Questions on Trigonometry59 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