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Hi-
If you are familiar enough with geometry and GPS coordinates to assist with this question then I'd sure appreciate the favor!
Given:
-a rectangle with long sides 1,742.4 feet long and short sides of 500 feet,
-four points on the corners we will call A,B,C, & D,
-known GPS coordinates for points A and B (short side, 500 feet apart)
-a 90 degree angle between the short sides and long sides
-GPS coordinates for point A of N 19*26.439' (....I am using the asterisk symbol for "degrees") and W 154*57.212'
-GPS coordinates for point B of N 19*26.510' and W 154*57.167'
...then, what are the GPS coordinates for points C and D?
The reason I ask is because I have a metal detector ready to go out and find the buried treasure at points C and D, those being metal stakes marking the property boundaries on a long narrow 20 acre lot on the Big Island of Hawaii, but where-ever points C and D are at they are buried under leaf litter and such like in the jungle. If we know the GPS coord then we can go direct to the vicinity and use the metal detector to locate the metal pins. We want to conserve and protect this patch of forest for the plants and critters therein.
Any GPS coords you can figure and send would be fantastic! (...I need to take off my shoes if I hope to count above ten, and am challenged if needing to go above 20...)
-Steven
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Re: Lat & Long Coords Question
Fri, July 24, 2009 - 11:22 AM
As it turned out I had one of those coordinates above wrong (transcription error from the field notebook) which in turn led to a bit of puzzlement in the figuring below, but this reply from a non-tribe friend is provided so the process he used can be seen. Once we figured out the correct coordinates on the front two pins then this process proved predictive for the back two pins.
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OK..it took some poking around, but this is what I come up with:
Assuming that point "C" is 1742.4 ft from point "B", it's coordinates are N 19 26.5100 W 154 56.8636 and point "D"'s coordinates are N 19 26.4390 W 154 56.9086....but I have some reservations:
Here's how I came up with this:
Step 1. First, I used boulter.com/gps/distance/ to verify that the distance between points A & B is 500 ft. (I actually got 501 feet..but close enough)
Step 2. Next, using the site williams.best.vwh.net/gccalc.htm , and the second computation function " Compute lat/lon given radial and distance from a known point", I entered the coordinates for point B as 19:26.510 in the "Lat1" field and 154:57.167 in the "Lon1" field, put 90 in the "Course 1-2" field (based on the 90 degree angle between short & long sides) and 1742.4 in the "Distance 1-2" field, yielding the coordinates N 19:26.5100 W 154:56.8636 .
(NOTE: I'm not totally sure about the "Earth model" field; there are several choices, but I used the default "WGS84/NAD83/GRS80" because I believe WGS84 is the standard for most GPS receivers)
Step 3. Then I went back to boulter.com/gps/distance/ to verify the above...giving a distance of .33 miles which converts to 1742.4 feet www.onlineconversion.com/lengt...on.htm
Step 4. Repeated steps 2-3 for for point A...and got N 19 26.4390 W 154 56.9086 for point D.
Then I took my new C & D coordinates and went back to boulter.com/gps/distance/ to verify distance between them, and voila! 501 ft
However...if we split the rectangle into 2 right triangles (a diagonal line from either A to C or B to D), the hypotenuse of either triangle should be 1812.72...but when I use boulter.com/gps/distance/ to verify distance between A & C, I get 2059.2 ft., and between B & D I get 1531.2 ft.....aaarrrghhhhh!!!!!
Wait a second....the only way to use the above tools to calculate this is to know the "true course" (radial) from the known points...basically, by using a "right angle" of 90 degrees (and wrongly assuming that it is the "true" course, we have created a trapezoid and thus have different diagonal measurements...90 degrees is "East", and the "true" direction we need is in a south-east heading, as we can tell from looking at the TMK map.
OK, maybe we can get what we need from the meets & bounds description on the deed. The deed calls out:
"measured from true south"..:
1. 307 degrees 28 minutes 30 seconds 1742.4 feet along Lot 2-C
2. 37 degrees 28 minutes 30 seconds 500 feet along Remainder Lot
3. 127 degrees 28 minutes 30 seconds 1742.4 feet along Lot 2-E
4. 217 degrees 28 minutes 30 seconds 500 feet along the road.
Using the site in step 2 above, and plugging in 307 (taken from the above deed meets & bounds description) for the "Course 1-2" field at williams.best.vwh.net/gccalc.htm, we get N 19 26.683 W 154 57.409 for point 'C". However, that point is in the wrong direction as we can see by entering that coordinate in on this site: www.geotruc.net/ (enter the coordinate & click Plot It!, then zoom in and you can see that this point is on the wrong side of the road.)
OK, using 127 instead, we get N 19 26.337 W 154 56.925 for point "C", and when going to www.geotruc.net/ we see that it's (at least) on the correct side of the road. Using 127 again to determine point "D", we get N 19 26.266 W 154 56.970.
Repeating step 3 to determine distance between our new C & D coordinates gives us 501 ft...hooray!
Unfortunately, we still end up with non-equivalent measurements of our new diagonals (A to C: .33 miles / 1742.4 ft, B to D: .35 miles / 1848 ft. ... also, the distance calculator generates a "miles" value that's rounded to 2 decimal places..the exact miles value should be .3433 to equal 1812.72 ft.) but it's way closer than when 90 degrees was used..
Anyway, I don't have complete confidence in this calculation, but maybe you can play around with these websites...