An aeroplane is flying at a height of 300m above the ground. Flying at this height the angles of depression
(April, 2017)
from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively.
Find the width of the river. [Use V3 =1.732]
(April, 2017)
Answers
width of river = 473.2 m
first of all, let's draw a rough diagram using given statement.
see figure, here A is the position of aeroplane such that AD = 300m and angles made at observations points B and C are 60° and 45° respectively.
we have to find width of bank of river i.e., BC
from ∆ABD,
⇒tan60° = AD/BD
⇒ BD = AD/tan60° = 300/√3 = 100√3 m
again from ∆ACD,
⇒tan45° = AD/CD
⇒CD = AD/tan45° = 300/(1) = 300m
then, BC = BD + DC = 100√3 m + 300 m
as given, √3 = 1.732
so, BC = 173.2 + 300 = 473.2 m
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