180°00´00´´ – (42°19´08´´ + 44°51´59´´ + 47°28´43´´), orS45°20´10´´W. The bearing of CD is equal to angle Cminus the bearing angle of BC.CoordinatesSuppose that you are tying the quadrilateral shownin figure 15-29 into a state grid system. The nearestmonument in this system lies 1,153.54 feet fromstation D, bearing S50°16´36´´W from D, as shown infigure 15-30. This means that the bearing from themonument to D is N50°16´36´´E. Suppose that the gridcoordinates of the monument are y = 373,462.27 feetand x =562,496.37 feet.The latitude of the line from the monument tostation D is 1,153.54 cos 50°16´36´´, or 737.21 feet. Thedeparture of the same line is 1,15354 sin 50°16´36´´, orFigure 15-30.—Coordinates.You would find the bearing of BC and CD similarly,except that you have to watch for the angle you are after.Always remember that a bearing angle does not exceed90° and is always reckoned from north or south. Tofind the bearing of BC, you must find the sum ofangle B (angles 3 and 4, fig. 15-28) plus the bearingangle of AB and then subtract it from 180°; you cansee that BC bears southwest, so just add thisdesignation to the proper place in the bearing anglefor BC. In this case, the bearing of BC will be887.23 feet.The y coordinate of station D equals the ycoordinate of the monument plus the latitude of the linefrom the monument to D, or 373,462.27 + 737.21, or374,199.48 feet. The x coordinate of station D equals thex coordinate of the monument plus the departure of theline from the monument to D, or 562,496.37 + 887.23,or 563,383.60 feet.Knowing the coordinates of station D, you can nowdetermine the coordinates of station A. The latitude ofDA is 700.00 cos 15°00´00´´, or 676.15 feet. Thedeparture of DA is 700.00 sin 15°00´00´´, or 181.17 feet.The y coordinate of station A is equal to the ycoordinate of station D plus the latitude of DA, orFigure 15-31.—Sun observation field notes.15-40
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