an aeroplane when flying at a height of 2000m from the ground passes vertically above a helicopter at an instant when their angle of elevation from the same point on the ground are 60° and 30° . find the vertical distance of the helicopter from the ground
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the vertical distance of the helicopter from the ground will be 2000/3 m
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AB = height of plane
DB = height of helicopter = x
BC = y
In triangle DBC,
tan 30 ° = DB/BC
= x/y = 1/√3
x√3 = y ...(1)
In triangle ABC,
tan 60° = AB/ BC
2000/y = √3
using (1)
2000/x√3 = √3
2000 = (x√3)√3
2000 = 3x
x = 666.66 m = height of helicopter from ground.
DB = height of helicopter = x
BC = y
In triangle DBC,
tan 30 ° = DB/BC
= x/y = 1/√3
x√3 = y ...(1)
In triangle ABC,
tan 60° = AB/ BC
2000/y = √3
using (1)
2000/x√3 = √3
2000 = (x√3)√3
2000 = 3x
x = 666.66 m = height of helicopter from ground.
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