# Determining property lines using actual measurements and county survey records

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 deg`
• `N/E = 84 deg 46 min`
• `E/S = 89 deg 98 min`
• `S/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.

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.

• The fact that the N and S sides are equal does not mean the other two sides are equal to each other. The reason is that the N and S sides are not parallel to each other. Draw a scale drawing using a mm ruler. A good scale would be 1 mm = 1 ft. Commented Aug 29, 2020 at 21:41
• To make a scale drawing you will need a good mm ruler and a protractor. Using trig you could avoid using a protractor, but this would be the hard way to do it. A compass would also help. Did you find the three corner markers you have found with a metal detector or by some other means? Commented Aug 29, 2020 at 21:58
• Some survey companies will give a very reduced rate for determining one property line. This is to facilitate the construction of a fence or retaining wall along a property line with an adjoining property. Commented Aug 30, 2020 at 0:20
• FYI the sum of the interior angles of any quadrilateral (four straight line sided figure) is 360 deg exactly. The individual angles can differ from 90 deg and the sides can all be different in length. Commented Aug 30, 2020 at 0:29
• The general "interior angles of a closed polygon" formula is (number of sides - 2) x 180 (180 for a triangle, 360 for a quadrilateral, 540 for a pentagonal, etc. and is a standard accuracy/sanity check on any survey of a closed traverse (such as land boundaries) Commented Aug 30, 2020 at 0:58

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.

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 "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'.

• The one caveat about relying on found rebars is that they may have been placed there by a homeowner and not by a surveyor. I did this once myself. I found three rebars on a residential lot but there was not a 4th. I measured parallel to the street curb the exact length shown in the county data and pounded in a 1/2" rebar. When we later had the property surveyed my bar was spot on according to the expert surveyor I hired. Commented Aug 30, 2020 at 0:37
• I will try two things: (1) Measure the distance between W/N rebar and E/N rebar, and (2) Try to find the fourth rebar (S/W) again. One of the main questions I have is whether geometrically (or is it trigonometrically), does it add up to have both `N=S=65.10` especially given all the angles. I don't think it does. I think the N should be longer than S based on the angles. If true, it would mean the original survey from 1960 is wrong. Commented Aug 30, 2020 at 0:52
• I see the OP's concern that the N boundary should be longer than the S. Maybe they did record the same number twice by mistake. I look forward to learning the result of his measuring the distance between the two north rebar markers. With that value we could calculate where to look for the 4th rebar. Commented Aug 30, 2020 at 6:54
• The N side is indeed longer than what the map says. See Edit 2. Commented Aug 30, 2020 at 15:11
• I recalculated using OP's 66'5" (66.417') for the N side, 107.5', 114.5' for W and E sides, and used only the two north angles 96 deg and 84 deg 6 min (84.1 deg). This gives 66.243' (66'3") for the S side. This shows that it is to be expected that for this lot the N and S sides are counterintuitively very nearly equal, with the N side only 2" longer. Why? The cosine function changes very little for small angles starting from 0 deg. Commented Sep 3, 2020 at 20:00

I think the units for the angles on the diagram are correct as degrees and minutes and are not decimal fractions of degrees. Taking them as degrees and minutes the interior angles add up to 360 deg exactly.

There are two errors in the OP's interior angles above: N/E should be 84 deg 06' and E/S should be 89 deg 58'. So going clockwise from NW the angles in decimal are 96.000 deg, 84.100 deg, 89.967 deg, and 89.933 deg which adds up to 360.000.

I made a scale drawing and found the angles and lengths are roughly consistent.

A trig formula (the cosine law) gives the diagonal SW - NE as 131.367 ft using the NW triangle versus 131.670 ft for the SE triangle. Probably the discrepancy is due to an error in the lengths reported in this old survey for the N or S boundaries of the lot. A new survey is needed.

Bottom line is that if you cannot find the 4th rebar marker, you should have the surveyor put one there as part of a new survey. Otherwise you risk encroaching on a neighbor's property or giving away part of yours.

If you can find the 4th rebar and you really want to save money, you could forego getting a new survey, but it might be best in the long run to get a new survey.

You could have the surveyor verify both E and W property lines, and give a copy of the survey to each of your two neighbors.

Edit

Final calculations:

I calculated using the following lengths CW starting from N side 66.417',114.5', 66.02', 107.5'. And using the following interior angles CW starting from NW: 96.000 deg, 84.100 deg, 89.967 deg, 89.933 deg. This gave 132.137 ft for the SW to NE diagonal from both triangles (by cosine law). Another trig formula (law of sines) gave 84.0 deg for the NE angle which is good agreement with the given value of 84.1 deg. The SW angle must therefore be in agreement too.

The area of the lot is approx 7326 sq ft from the formula for the area of a trapezoid: perpendicular distance between the parallel sides times the average of the lengths of the parallel sides. 66(107.5 + 114.5)/2.

EDIT2

The two south corners of this lot are so close to 90 deg angles that for most purposes they can be considered 90 deg angles. This means the W and E property lines are very close to parallel. The northern angles being 96 and 84 deg are off from 90 deg far enough so the N and S property lines are not parallel. The shape of this lot then is very, very close to a trapezoid and not too far from being a rectangle. I would describe it as trapezoidal, nearly rectangular.

• Did you first split the plot into 2 triangles to make these calculations? In any case, the county map lists the total area to be 7110 sqft. That's a difference of 216 sqft. Commented Aug 31, 2020 at 13:21
• Yes, I split it into two triangles sharing the SW - NE diagonal. I used all the angles given on the diagram, the lengths of the E and W sides from the diagram, and your measurement of the N side. This allows calculation of the length of the S property line as 66.0 ft. Have you dug at 66 ft? Commented Aug 31, 2020 at 16:08
• There might not be a 4th rebar marker on your property. It might never have been there or someone one might have removed it, perhaps when installing a fence post. Our lot in a tract development had four rebar corner markers. A relative's lot in the same development had only three (until I added a 4th). Commented Aug 31, 2020 at 16:25
• There are a number of possible ways the city value could be different from what I have gotten. Only a full new survey would settle the matter. A new survey could report slightly different values for the angles and for the lengths of the W and E sides. A new survey might show that the existing three rebars are not exactly on the corners. This is not likely but is not impossible. Commented Aug 31, 2020 at 16:37
• Yes, I dug a two feet diameter hole around ft. 66 in the S/W corner. My magnetic detector gives a very strong signal in the hole. But I am reluctant to dig deeper as it might be coming from any utility pipes underneath. Commented Aug 31, 2020 at 17:20

Following is a simplified calculation of the length of the S property line:

1. Treat the two south corners as right angles (from old survey diagram).

2. From the old survey diagram take the NW interior angle as 96 deg and the lengths of the W and E sides to be 107.5 ft and 114.5 ft, respectively.

3. Take the OP's measurement of the N side 66 ft 5 in or 66.417 ft.

4. Divide the lot into a rectangle of length 107.5 ft (and width W as yet unknown) and a right triangle with one angle 6 deg and opposite side 7.0 ft.

5. Base of triangle = 66.417 ft x cos (6 deg) = 66.05 ft = W

6. So S line is 66.0 ft long. (66.05 by simplified calc and 66.02 by more involved calc)

7. Area of lot = area of rectangle + area of triangle = (107.5 x 66) + (1/2 x 66 x 7) = 7095 + 231 = 7326 sq ft

EDIT

If the only new fence you want to install is in the front half of the lot, then there would not be much risk in putting in a temporary rebar or wooden stake in the SW corner at 66.0 ft from the existing rebar in the SE corner (and 107.5 ft from the existing rebar in the NW corner).

But if you would sight along this presumed West property line and see encroachment by structures of your neighbor, then you would be advised to not proceed further without a new survey. You don't want to encroach on your neighbor's lot. For one thing this could complicate your proposed sale in 2 years.