Question 43

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

Solution

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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