Q. 34

The two palm tree

Answer :


Let BD = river


AB = CD = palm trees = h


BO = x


OD = 80 - x


In ΔABO,


tan60°= h/x


√3 = h/x -----------------------(1)


h = √3x


In ΔCDO,


tan 30°= h/(80 - x)


1/√3 = h/(80 - x) ---------------------(2)


Solving (1) and (2), we get


x = 20


h = √3x = 34.6


the height of the trees = h = 34.6m


BO = x = 20m


DO = 80 – x = 80 – 20 = 60m


OR



Let AB = Building of height 50m°


RT = tower of height= h m


BT = AS = x m


AB = ST = 50 m


RS = TR – TS = (h - 50) m


In ΔARS, tan30°= RS/AS


1/√3 = (h-50)/x -------------(1)


In ΔRBT, tan60°=RT/BT


√3 = h/x --------------(2)


Solving (1) and (2), we get


h= 75


from (2)


x = h/√3


= 75/√3


= 25√3


Hence, height of the tower = h = 75m


Distance between the building and the tower = x = 25√3 = 43.25m


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 Distances - IHeights and Distances - IHeights and Distances - I54 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