I'm going to make a huge guessing leap about this lab work and imagine that you are dealing with a tungsten lamp and that your lab trainer made a resistance measurement of the lamp, when cold; but you then made voltage and current measurements with the lamp active and hot.
From your numbers, I find \$\frac{5.795\:\text{V}}{36.2\:\text{mA}}= 160.082873\:\Omega\$. That is also what you got when you arrived at the calculated section (of your workbook?)
The issue then is that the resistance measurement was taken under different conditions. The trainer resistance measurement was made with a cold filament, as the trainer resistance measurement uses a very small current. The trainer voltage and current measurements were taken after the filament had enough time to heat up and glow, and was at the time quite hot.
The specific resistance of tungsten varies from, for example, \$5.00\times 10^{−6}\:\Omega\cdot\text{cm}\$ at \$273.15^\circ\text{K}\$ to \$117.1\times 10^{−6}\:\Omega\cdot\text{cm}\$ at \$3655^\circ\text{K}\$. A more detailed table can be found at this hypertextbook page:
Image may be NSFW.
Clik here to view.
Assume for now that your resistance measurement of \$29.3\:\Omega\$ was made at about \$300^\circ\text{K}\$. The ratio of resistance (cold vs hot) is \$\frac{160.1\:\Omega}{29.3\:\Omega} \approx 5.464\$. If you look up that ratio on the above table then I think you will find that the likely temperature of the filament, when active and hot, is \$1200^\circ\text{K}\$.
This is likely all you need to explain the results you have provided in your question. Both measurements were correct. They just weren't made under the same experimental conditions.
