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Question
An aeroplane at an altitude of 200 m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.
Solution
Let AD be the height of the aeroplane and BC = x m be the width of the nver.
Given: AD=200m
In ΔABD
`"AD"/"BD" = tan45^circ`
⇒ `"AD"/"BD" = 1`
⇒ AD = BD
⇒ BD = 200m (∵ AD = 200m)
Now ,
In ΔACD
`"AC"/"CD" = tan60^circ`
⇒ `"AC"/"CD" = sqrt(3)`
⇒ `"CD" = "AC"/sqrt(3) = 200/sqrt(3)`
⇒ `"BC" = "BD" + "CD" = 200 + 200/sqrt(3) = 200 + 115.47`
⇒ `"BC" = 315.4` m
Thus, the width of the river is 315.4 m.
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