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Figure 7-8.Latitude and departure. - 14071_131

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Figure 7-8.—Latitude and departure. The latitude of a traverse line means the length of the line as projected on the north-to-south meridian running through the point of origin. The departure of a traverse line means the length of the line as projected on the  east-to-west  parallel  running  through  the  point  of origin. To understand this, you should examine figure 7-8. The point of origin is at  O. The line  NS is  the meridian through the point of origin; the line  EW is the parallel through the point of origin. The latitude of  AB is the length of AB as projected on NS; the departure of AB is the length of AB as projected on EW. You can see that for a traverse line running due north and south, the latitude would equal the length of the line and the departure would be zero. For a line running due east and west the departure would equal the length of the line and the  latitude  would  be  zero. Now, for a line running other than north to south or east to west, you can determine the latitude or departure by simple triangle solution. Figure 7-9 shows a traverse line 520.16 feet long bearing S61°25'E. To determine the latitude, you solve the triangle ABC for the length of the side AC. From the bearing, you know that the size of  angle  CAB  (the  angle  of  bearing)  is  61°25'.  The triangle is a right triangle; therefore AC  =  520.16  cos  61°25'  =  248.86 ft. The latitude of a traverse line, then, equals the product of the length of the line times the  cosine of the angle of bearing. To determine the departure, you solve the triangle for the length of the side CB shown in figure 7-10. CB = 520.16 sin 61°25'  = 456.76 ft. Figure 7-9.—Latitude equals length of traverse line times twine of angle of bearing. Figure 7-10.—Departure equals length of traverse line times sine of angle of bearing. The  departure  of  a  traverse  line,  then,  equals  the length of the line times the sine of the angle of bearing. The latitude of a traverse line is designated north or south and the departure is designated east or west following the compass direction of the bearing of the line. A line bearing northeast, for example, has a north latitude and east departure. In computations, north latitudes are designated plus and south latitudes minus; east departures are designated plus and west departures minus. 7-9



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