A person, standing on the bank of a river, observes that the angle of elevation subtended by a tree on the opposite bank is 60o. When he moves 20 m away from the bank, he finds the angle to be 30o. Find the breadth of the river.
The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from top of the second tower is 30o. If the height of the second tower is 60 m, find the height of the first tower.
Let AB be the width of the river and BC be the tree of height h metres (say). Let D be the point 20 metres away from the bank of the river and let AB=x metres.
tan 60o = = h = x … (1)
tan 30o = … (2)
From (1) and (2),
3x = x + 20
x = 10
Thus, the breadth of the river is 10 metres.
Let the distance between the two towers AB and CD is 140m.
DE = CB = 140 m
Height of the second tower CD = 60 m
Let the height of first tower, AB, be h m.
CD = BE = 60 m
AE = (h - 60) m
= tan 30o
h - 60 = 140
h = 140 + 60
h= 80.83+60 = 140.83m
Thus, the height of the first tower is 140.83 m.
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