Q8 of 35 Page 219

A person standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank has measure 60. When he retreats 20 m from the bank, he finds the angle to have measure 30. Find the height of the tree and the breadth of the river.



Let PM be the tree. OM represent the width of the river.


So, ∠PMO = 90⁰ and OA = 20 m


Let OM = Breadth of the river = x and


PM = Height of a tree = h


AM = OM + OA = x + 20


In ∆PMO,




H = √3x …………(1)


In ∆PAM,



……………(2)


From (1) and (2) we get,



X + 20 = √3x × √3


X + 20 = 3x


3x – x = 20


2x = 20


X = 10


Now, h = √3x


= 1.73 × 10


= 17.3


The breadth of the river = OM = x = 10 m and


The height of the tree = PM = h = 17.3 m


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