I am currently in the process of determining the exact dimensions of my property in order to install a fence. I have located three marker pins, though not the fourth one yet.
After searching through county records and talking to a private surveyor, I have laid my hands on two plat maps, which are different in some important detail.
Imagine a uneven rectangle, which is taller than wider. Sides west, north, east and south appear respectively as W, N, E and S below:
W = 107.5'N = 65.1'E = 114.5'S = 65.1'
In the county map, only W and N side measurements appear, whereas the surveyor map shows all four. Angles are as follows:
W/N = 96 degN/E = 84 deg 46 minE/S = 89 deg 98 minS/W = 89 deg 56 min
County map shows no angles. Surveyor map shows first and the last angles. I calculated the remaining two angles by extrapolation using angles for the adjoining property. The angles do add up to 360: 96 + 84.46 + 89.98 + 89.56 = 360 deg.
However, do the property line lengths make sense geometrically speaking? If N and S are both 65.1', then wouldn't W and E would also have to be identical? But one is longer than the other by 7 ft.
Either the angles are incorrect or the sides are. I basically need to draw a rectangle with these lengths and see if the angles come out right.
Edit1:
Picture of original survey from 1960
Edit2: The actual measurement between the NE and NW rebars is 66'5", which is little over a foot longer than what the map says. I wish I knew trigonometry better so I could precisely calculate the difference made by the two angles (90 deg vs 96 deg.).
Edit 3: I tried to find the S/W marker pin again. Measured roughly 65' from the S/E pin and dug up very carefully with hand tools. All I have found is remnants of the previous chain link fence post in concrete. It's exactly in the same spot where I was hoping to find the pin. The current fence doesn't quite extend until there (space for trash bins etc.). The metal detector continues to provide very strong signal next to the post in the hole. I must call 811 before I continue on.
Best Answer
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 "here it really is.")
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.
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 "calculated" 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 "geometrically speaking" 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'.