mechanics (calculating plane speed and climb angle
posted by royston .
Two radar stations A and B, are separated by the distance a = 500 m, track the plane C by recording the angles α and β at 1second intervals. If three successive readings
are
t (s) 9 10 11
α 54.80◦ 54.06◦ 53.34◦
β 65.59◦ 64.59◦ 63.62◦
calculate the speed v of the plane and the climb angle γ at t = 10 s.
The coordinates of the plane can be shown to be,
x = a*((tan β)/(tan β − tan α))
y = a*((tan α tan β)/(tan β − tan α))

maybe I'm missing something, but if angles α and β are in the xy plane, how do we figure the altitude of the plane, and hence any climb rate? No mention is made of altitude, either of the radar stations, or of the plane.
No figure here, so I'm not sure of the 3D layout. 
nikaw