Hi all. Still dubbing away at my self guided education. Harder than ever with a full time job. I am attempting to confirm my calculations of the width of a Right of Way corridor, as measured along a property line. See attached. I've done the math using the formulae for an obtuse scalene triangle. 10th grade geometry, yes, but still a brain challenge.
CAD seems to confirm the same thing. Can anyone confirm my math? Thanks in advance!
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Welcome back after 2.5 years.
I'm on my phone-may check calcs when at desk.
I agree, getting 57.778 ft, but am a bit nervous about expressing it so precisely given even foot inputs.
So, given the precision of the numbers on the survey, i.e. "80.0'", "Radius=150.0'" etc., the proper precision of the calcs. would be 69.9' and 127.7', rendering the distance between them 57.8'?
I just looked at the sketch at first.?ÿ Seeing now that those are design values and not measurements, then the design value for your distance can be to any precision, but what is put on the ground by measurement will have its own degraded precision.
Thanks Bill!
I'd love it if someone could confirm the three dimensions in CAD (vs. geometric calcs); i.e Distance from the corner to the near side of the ROW: 69.943; Distance to the far side of the ROW: 127.720, making the "width" of the ROW as measured along the property line 57.78'.
I surveyed the driveway long ago and always assumed it was in the center of the ROW and never bothered surveying the ROW. That appears to be not the case. My suspicion is that the ROW was "created" in CAD completely...never staked on site. Then when mr. bulldozer guy put the driveway in, he paid attention to the topography, not the survey...In some places the driveway departs completely from the bounds of the ROW.
I added some more bearings and distances to my file, and get 69.941, 127.718, and?ÿ 57.777 all close enough to your numbers.
But I can't close the loop of the driveway center lines and the road right of way line.?ÿ They miss by almost 25 ft at the cul-de-sac.?ÿ Either I copied or interpreted something wrong or it's sloppy.?ÿ What is the bearing on the 302.8 ft line?
@bill93 :
It's N25-55-05E. Our property line ends on the 1,680.2' line, so I've been concentrating for now on A to B. I have a later survey that another surveyor did recently that updates the right of way. It's quite amazing what he did to get the "new" right of way to match the deeded right of way.
Can't do CAD, but here's what Geogebra (a free on-line math teaching software) gives.
Note that 4 concentric circles and a triangle describe the figure graphically. As long as the 112.78 degree angle is held constant, the triangle can be rotated about the center to any orientation without changing the numbers.
Construction wise, the center of the circles is at (200,200). Point A is arbitrarily placed on the 80-foot radius circle and then point O prime is determined by the 112+ degree angle. Intersection points are marked and the software provides the measurements.
So the only inputs are the fundamental measurements. The black box does the rest.
Hope this helps.
@rfc :?ÿ The red and purple numbers and segments in the drawing below are what I think you're asking about. Pretty close to Bill's numbers and to yours. Who knows what goes on in different black boxes.
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@mathteacher Thank you, Sir! That's the "cleanest" depiction of the problem I've seen. I'll check out Geogebra on line. Now that the numbers are confirmed I'll move on to staking it in the field, and mapping the existing driveway. Thank you also, @bill93.
@mathteacher those Geogebra sketches are beautiful!
It's great software. Sort of CAD light double light with a ton of higher math functions. The burning pedagogic question for me was whether to incorporate learning Geogebra into the class or just use it to create precise drawings that made sense to students.
I opted for the second option simply because the amount of material we had to cover used up all the class time. We needed a separate little 30 minute slot ever day for teaching usable tech, but that never happened. Pep rallies and such did, though.
@mathteacher I shared a link with my HS senior.?ÿ He probably thinks I am ultra cool now.
Did a HS senior ever think Dad was cool?
And if he did, he probably wouldn't say cool now.?ÿ It's so 1970's.?ÿ There has to be a new word.
@bill93 one of the new words for cool is ??sick.?
So, as it turns out, the ACTUAL included angle between the boundaries is 108.945 degrees, not 112.78 degrees. Using that angle, I now get 73.524' first point, 131.823' to the second point, for a width of the ROW measuring 58.299'.
Do I assume correctly that in such situations, you'd hold actual measurements rather than those from an "ancient" survey, done in the office?
I can duplicate your numbers by changing the bearing from N52?ø 47'E to approximately N48?ø 56' 42"E.?ÿ Are you basing this on monuments at the road ROW and 2k feet SW, or what?
@bill93?ÿ
The bearing of the 80' segment is actually S55-55-16 East, and the bearing from the point 2k sw to the corner is N53-01-28. These come from COGO from my survey. The dilemma is that the original survey, including the description of the ROW shows otherwise. So do you use the described (but inaccurate) numbers, or the "real" numbers?
You use any monuments that seem original. You assume bearings on a plat are all relative to some arbitrarily chosen reference that isn't actual north, unless the plat explicitly gives another basis of bearings.
When nothing fits, you look for obvious copy errors, like the one I mentioned in arecent thread where 201.1 ft measures to be 210.1 ft.
And when nothing makes sense, you and your adjoiner sit down and decide what's a reasonable solution.