Question
Download Solution PDFAn aeroplane at an altitude of 3000 m observes the angles of depression of opposite points on the two banks of a river to be 45 and 60 respectively. Find the width of the river in metre.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Height of aeroplane (altitude) = 3000 m
Angles of depression to opposite banks = 45° and 60°
Diagram understanding:
Let the points on the banks be A and B.
Let point C be the position of the aeroplane vertically above point D on the river.
Angle of depression to point A = 45° → triangle CAD
Angle of depression to point B = 60° → triangle CBD
Formula used:
In right triangle: tanθ = perpendicular / base
Calculations:
From triangle CAD (angle = 45°): tan 45° = 3000 / AD ⇒ 1 = 3000 / AD ⇒ AD = 3000 m
From triangle CBD (angle = 60°): tan 60° = 3000 / BD ⇒ √3 = 3000 / BD ⇒ BD = 3000 / √3 = 1000√3 ≈ 1732.05 m
Total width AB = AD + BD = 3000 + 1732.05 = 4732.05 m ≈ 4730 m
∴ The width of the river is approximately 4730 m.
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