Q. 185.0( 14 Votes )

The angle of elev

Answer :


Let P and Q be the two positions of the aeroplane 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.


PAB = 60° and QAB = 30°


Also given PB = 3000√3 m


In Δ ABP,


tan 60° = BP/AP


√3


AB = 3000 m


In Δ ACQ,


tan 30° = CQ/AC



AC = 3000 (3)


AC = 9000 m


Distance, BC = AC – AB = 9000 – 3000 = 6000 m


Thus, the plane travels 6000m in 30 seconds.


We know that speed = distance/time


Speed of plane = 200 m/sec


Speed of the aeroplane is 200 m/sec.


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