An aeroplane is flying at a height of 300m above the ground. Flying at this height,the angle of depression from the aeroplane of two points on banks of a river in opposite directions are 40° and60° respectively. Find the width of the river? (root3=1.732)
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Solution:
Let P be the position of the aeroplane and let A and B be
two points on the two banks of a river such that the angle of depression at A and B are 60°
and 45° respectively.
Let AM = x m and
BM = y m.
We have to find ,
Width of the river AB .
i) In ∆APM, we have
tan60° = PM/AM
=> √3 = 300/x
=> x = 300/√3
Rationalising the denominator, we get
= [(300×√3)/(√3×√3)
= 300√3/3
= 100√3
= 100×1.732
= 173.2 m ----(1)
ii) In ∆BPM, we have
tan45° = PM/BM
=> 1 = 300/y
=> y = 300 m----(2)
From equations (1) & (2) , we get
AB = x+y
= 173.2 + 300
= 473.2 m
Therefore,
The width of the river = 473.2 m
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here is ur answer
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