Hey! An easy sum!
Geometry
Level
pending
From an aeroplane vertically above a straight road the angles of depression of two consecutive kilometrestones on opposite sides of the plane are observed to be 60 degrees and 30 degrees, respectively. Find the height of the aeroplane above the road, in integral metres.
The answer is 433.
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1 solution
The problem is very easy. 1km=1000m
Let the height of the aeroplane be h m.
Let the distance on the consecutive sides be x and 1000-x respectively.
tan60°= h/x
Or root 3x =h
And tan30°= h/1000-x
Or Root 3h=1000-x
Or3x = 1000-x from the other equation
Or 4x=1000
Or x=250
Now Root 3 x =h
Or root 3 *250= 433
Answer 433