A man standing at a point X on the bank XY of a river that cannot be crossed observes a tower to be ...........

Quantitative Aptitude (CDS) Trignometry

A man, standing at a point X on the bank XY of a river that cannot be crossed, observes a tower to be N $\alpha$ ⁰ E on the opposite parallel bank. He then walks 200 m along the bank to the point Y towards East, and finds the tower to be N $\beta$ ⁰ W. From these observations, the breadth of the river will be

(Given that tan $\alpha$ ⁰=2 and tan $\beta$ ⁰=0.5)

60 m

70 m

80 m

90 m

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Explanation:

Here, AB is the breadth of river.
In triangle ABX:
tanα0 = AB/XB= h/x => 2 = h/x => x= h/2
In triangle ABY:
tanβ0 = AB/BY= h/y=>0.5= h/y => y=2h
Given, x + y = 200
=>h/2+2h=200
=>h=200×25=80
Hence the breadth of river be 80 m