the angle of elevation of an aeroplane is from a point p on the ground 60 degree after 12 seconds from the same point p the angle of elevation of the same plane changes to 30degree.if the plane is flying horizontally at a speed of 600√3km/hr,find the height at which the plane is flying.
Answers
Let P and Q be the two positions of the plane and A be the point of observation. Let ABC be the horizontal
line through A. It is given that angles of elevation of the plane in two positions P and Q from a point A are
60° and 30° respectively.
So, ∠PAB = 60°, ∠QAB = 30°
Again given that PB = 1500√3 m
In ΔABP, we have
tan 60° = BP/AB
=> √3 = 1500√3/AB
=> AB = 1500 m
In ΔACQ, we have
tan 30° = CQ/AC
=> 1/√3 = 1500√3/AC
=> AC = 1500√3 * √3 = 1500 * 3 = 4500 m
Now, Distance = BC = AC – AB = 4500 m – 1500 m = 3000 m
Thus, the plane travels 3000m in 15 seconds
Hence, speed of plane = 3000/15 m/sec = 200 m/sec
= (200/1000) * 60 * 60
[Since 1 km = 1000 m, 1 hr = 60 minutes = 60 * 60 seconds]
= 3600/5
= 720 km/hr.