An aeroplane at an altitude of 200 metres 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.
Let the position of the aeroplane be A, B and C be two points on the two banks of a river such that the angles of depression at B and C are 45° and 60° respectively. Let BD = x m, y m andAD = 200 m.
In right triangle ABD, we have
In right triangle ACD, we have
Adding (i) and (ii), we get
Hence, the width of the river is 315.4 metres.
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Formula used:
tanθ = Perpendicular/Base
tan60° = √3
Calculation:
Let AB be the pole and BC be its shadow.
Let the length of shadow be x and the length of the pole be √3x.
Now, in ΔABC, let θ be the angle of elevation of the sun
⇒ tanθ = AB/BC
⇒ tanθ = √3x/x = √3
⇒ θ = 60°
∴ The angle of elevation of the sun at the time of shadow is 60°.
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