Determining property lines using actual measurements and county survey records
If you can find the 4th pin by poking around where the measured distances from the other two pins adjoining it indicate, it rules (the actual pin, or traces thereof, if extant, is the highest form of land surveying &quot;here it really is.&quot;)
Why yes, I did read Breed and Hosmer for fun once upon a time...
You basically pin a tape measure to the adjacent corners, mark an arc, and go looking with your metal detector near where they cross. If you can rent or borrow a transit and set it up properly you could do the same thing by turning the angles between the opposite pin and where the missing pin should be from each adjacent pin.
In neither case is it legal for you (in almost any jurisdiction) to set a replacement pin if you can't find the original, unless you were already a licensed surveyor (and you wouldn't be asking if you were); however, it is perfectly acceptable for you to refine your search for the missing pin.

E/S = 89 deg 98 min

No. 89.98 degrees, perhaps. If you see more than 59, it's not minutes or seconds of arc; it's fractional. Surveyors do not write 90 degrees and 38 minutes as 89 degrees and 98 minutes. Since it adds up correctly as fractional degrees, that's two indications that fractional degrees are what you have here.
Edit: But now that we can see the survey map, you &quot;calculated&quot; the number in question. Incorrectly, I do believe - since you just subtracted from 180 you got consistent, but incorrect numbers that added up nicely. 96°+ 89°-56'+ 89°-58'+ 84°-06' is the correct set of angles that correctly adds up to 360°-0' (96+84 =180 and the 6' split into 2' and 4' gets the other two angles to 90 is the way I do it in my head, use paper if it helps you.) So the angles on the survey are in degrees and minutes. This will matter.
As for &quot;geometrically speaking&quot; note that you do not have a rectangle. You have something vaguely rectangular, with no actual 90 degree corners. 96 degrees makes a rather large difference compared to 90 degrees...as does 84°-06'.