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Here are the data from the survey plan:

TIE LINES from BLLM No. 3, PLS 561, to corner "1" of:

LOT ----------Bearing--------------------Distance  
Boundary ----S 36deg 41min W ------11,641.21 meters  

BOUNDARY: 

LINE ----- BEARING ------------- DISTANCE   
1-2 ------ N 37deg 58min E ----- 251.18 meters  
2-3 ------ S 50deg 42min E ----- 199.73 meters  
3-4 ------ S 38deg 28min W ----- 248.00 meters  
4-1 ------ N 51deg 37min W ----- 197.58 meters  

Obviously the map has 4 points. If only I can get the lat-long reading of point 1 so that I can readily verify "on field" if it did not overlap to adjacent lots. Additionally, if lat-long coordinates of point 1 is known, I can easily check on the other three points and determine its position thru Bearings describe in the title/map.

I only need the process on how to do this, but it there is an application or software to do this, much better.

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    The origin is stated as 'BLLM No. 3, PLS 561', you need to find PLS561 to get the origin coordinate then you're about 11k from that by bearing/distance. Surveyors love to tie their surveys into existing surveys or known permanent survey marks for neatness; the accuracy of the surveys and known marks can change (be more refined) over time the survey remains the same (but changes with it) as a relationship, if the origin was set as an absolute it wouldn't move with the mesh and would very quickly become 'wrong' – Michael Stimson Jun 12 '15 at 3:12
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    That's how I read it. Whether PLS-561 is a permanent survey mark or existing survey I can't tell. – Michael Stimson Jun 12 '15 at 3:33
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    It depends on the survey and monumentation process. Not all monuments have lat/long, and those that do are only based on a particular survey date/network. More information about the location/country would be needed to suggest anything further, but as Michael said, "BLLM No. 3, PLS 561" is a monument or survey control point from a network with known coordinates of some kind. – Chris W Jun 12 '15 at 4:05
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    Welcome to GIS SE. You seem to have two or three questions here: (1) How do i get the coordinates of BLLM No. 3, PLS 561? (2) How do i compute lot coordinates from survey metes? (3) How do i convert survey grid coordinates to geographic lat-long? – Martin F Jun 16 '15 at 15:14
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    You might use the NGS survey mark app to find ones in the area. Maybe you'll be able to link up the name (I wonder if it's BLM rather than BLLM?). – mkennedy Jun 16 '15 at 17:55