Plant a vertical stick of known height on flat, level ground. At solar noon (when the shadow is shortest), measure the shadow length with a tape measure.
At solar noon on the equinox, the shadow formula is simple:
$$\text{shadow} = \frac{\text{stick\_height}}{\tan(90^\circ - \text{latitude})}$$
This is a direct consequence of the sun being over the equator on a sphere. Verify it with the NOAA Solar Calculator.
The flat model predicts a different shadow length. Go outside and measure. One of them is wrong.