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A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he walks 40 metres away from the tree the angle of elevation becomes 30°. The breadth of the river is
Let the height of tower be h m.
Let x be the distance from the bottom of tower to the point where it makes 60 degrees angle [also breadth of the river]
Applying in right triangle:
tan 60 = h/x
x = h/root3
and
tan 30 = h/x+40
Putting value of x in above equation, we get
h = 20 root3
and x = 20 metres
So, breadth of the river = 20 metres.
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