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I agree. Perhaps you could add language explaining that observations in the "real world" may differ from these results because of refraction.
I do note that you have the assumption stated that light is traveling in a straight line, but it would help if this were made more clearly.
Should you not be accounting for refraction when calculating the hidden height? This is explained by Andrew Young here:
https://aty.sdsu.edu/explain/atmos_refr/horizon.html
https://aty.sdsu.edu/explain/atmos_refr/bending.html
If you aren't going to include this in the calculation then you at least need to state so clearly on the calculator page.
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