An aeroplane (A) when flying at a certain height from the ground passes vertically above another aeroplane (B) at an instant when the angles of the elevation of the two aeroplanes from the same point on the ground are 30° and 45° respectively and the distance between two aeroplanes is 1000 m. Then, the approximate vertical height of the aeroplane A is
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Answers
Answer:
2500 for sure
Given : An aeroplane (A) when flying at a certain height from the ground passes vertically above another aeroplane (B) at an instant when the angles of the elevation of the two aeroplanes from the same point on the ground are 30° and 45° respectively and the distance between two aeroplanes is 1000 m.
To Find : approximate vertical height of the aeroplane A is
Solution:
Let say Height of Aeroplane A from ground = h m
Height of Aeroplane B from ground = h + 1000 m
Let say horizontal distance of viewing point from airplanes = D m
Tan 30° = h/D
=> 1/√3 = h/D
=> D = h √3
Tan 45° = (h+1000)/D
=> 1 = (h+1000)/D
=> D = h + 1000
Equate D
=> h √3 = h + 1000
=> h (√3 - 1) = 1000
=> h = 1000/ (√3 - 1)
=> h = 500 (√3 + 1)
=> h = 1,366 m
Height of Aeroplane A = 1366 m
approximate vertical height of the aeroplane A is 1366 m
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