Robert:
The reactive part of the signal is the part which is in phase with the triangular current; which, when differentiated by the (separate, preferably IB) receive coil, becomes a rectangle.
If you could subtract that rectangle out, then what would be left is the resistive components which are at 90 degrees with respect to the current. Since we're not talking a single sinusoid here, but a superposition of sinusoids, the signal you'd see in the time domain would a bit of a mess. And, it would be highly dependent on the shape and orientation of the iron.
One way to answer this question, is to get hold of a Fisher Impulse, which transmits pulses which have a triangular current waveform, make an air coil several inches in diameter, hook it up to a 'scope with a suitable damping resistor in parallel, slide it over the edge of the Impulse loop until you find a position of induction balance, and then bring a piece of iron into the field.
This technique is not limited to the Impulse, but I mention the Impulse because your question related to triangular current waveforms.
If you were thinking of a continuous triangular current waveform, Fisher CZ's do that. Same trick can be used with a CZ to see its response in the time domain on a 'scope.
--Dave J.