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Question

A vertical pole stand at a point O on a horizontal ground. A and B are points on the ground 10 m apart The pole subtends an angle 30 and 60 at A and B respectively . Then height of tower equals

A
103 m
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B
53 m
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C
153 m
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D
None of these
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Solution

The correct option is B 53 m
Given that:
PAO=30,PBO=60,AB=10 m
To find:
Height of the tower h=?
Solution:
Let PO be the height of the tower.
In PAO
tanPAO=POOA
or, tan30=hOA
or, OA=3h ............(i)
In PAO
tanPBO=POOB
or, tan60=hOB
or, OB=h3 ............(ii)
From eqn. (i) and (ii),
AB=OAOB
or, 10m=3hh3
or, 103m=3hh
or, 2h=103 m
or, h=53 m
So, Height of the tower =53
Hence, B is the correct option.

642949_299360_ans_657f0bc527c742fa91f36a531ac0edfe.png

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