An aeroplane, when 3500m high passes vertically above another plane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 45 degree and 30 degree respectively. Find the vertical distance between the two aeroplanes
Answers
Given : An aeroplane, when 3500m high passes vertically above another plane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are 45°and 30°respectively.
To FInd : the vertical distance between the two aeroplanes
Solution:
Let say
A Position of above plane
B position of lower plane
C is the point at ground below plane
D is the point of observation
AC = 3500
AB = distance between the two aeroplanes
Tan 45 = AC/CD
=> 1 = 3500/CD
=> CD = 3500
Tan 30 = BC/CD
=> 1/√3 = BC/3500
=> BC = 3500/√3
AB = AC - BC
=> AB = 3500 - 3500/√3
AB = 3500 (√3 - 1)/√3 = 1479.3 m
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