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Question
An aeroplane, at an altitude of 250 m, observes the angles of depression of two boats on the opposite banks of a river to be 45° and 60° respectively. If the boats are on the opposite sides of the aeroplane, find the width of the river. Write the answer correct to the nearest whole number.
Solution
Let A be the position of the airplane and let BC be the river. Let D be the point in BC just below the airplane.
B and C be two boats on the opposite banks of the river with angles of depression 60° and 45° from A.
In ΔADC,
`tan 45^circ = (AD)/(DC)`
`=> 1 = 250/y`
`=>` y = 250 m = DC
In ΔADB,
`tan 60^circ = (AD)/(BD)`
`=> sqrt(3) = 250/x`
`=> x = 250/sqrt(3)`
= `(250sqrt(3))/3`
= `(250 xx 1.732)/3`
= 144.3 m = BD
∴ BC = BD + DC
= 144.3 + 250
= 394.3 ≈ 394 m
Thus, the width of the river is 394 m.
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