Line impedance is not the same as a series resistance which would cause a voltage drop. Line impedance, altough it happens to be measured in ohms, tells how the electric and magnetic fields are related outside the wires (=in the space where the wave actually travels, it's not in the metal). You can use the line impedance in calculations of what happens to a wave in line joints and terminations, but it has no use in ohms law.
In ordinary 2 wire cables, but not in waveguides, you can make most of the wave calculations by using the voltages and currents which they cause to the wires, but remember, that the wave and thus also the actual energy flow is outside the metal, it's only guided by the wires.
In your case the wave comes from the source, which obviously has very low internal series resistance. The wave meets the matched load, no reflection is caused. If the signal is DC, the rest can be calculated with ohms law. You get full voltage if the wire hasn't remarkable DC resistance.