Suppose that you have some unknown DUT, a green box, and observed the waveforms V(v1) and V(v2) with your oscilloscope. Looking closely, you see that V(v2)/V(v1)=1.118 and that V(v2) is advanced in relative to V(v1) with 26.56 deg.
You will also see that by comparing the green trace, V(v2)-V(v1), and the red trace, V(v1), the amplitude of the green is just half of the red, and the green is exactly 90 deg in advance. (Note that the red and the yellow cross each other, which means the green is zero, at the peak of the red.)
Now that you have enough information to know Z(DUT), you will close your eyes and think very hard…
After a few seconds, you will say, “Eureka! Z(DUT)=30+j40 [ohm].”