Figure 7-8.—Latitude and departure.The latitude of a traverse line means the length ofthe line as projected on the north-to-south meridianrunning through the point of origin. The departure of atraverse line means the length of the line as projected onthe east-to-west parallel running through the point oforigin. To understand this, you should examine figure7-8. The point of origin is at O. The line NS is themeridian through the point of origin; the line EW is theparallel through the point of origin. The latitude of ABis the length of AB as projected on NS; the departure ofAB is the length of AB as projected on EW. You can seethat for a traverse line running due north and south, thelatitude would equal the length of the line and thedeparture would be zero. For a line running due east andwest the departure would equal the length of the line andthe latitude would be zero.Now, for a line running other than north to south oreast to west, you can determine the latitude or departureby simple triangle solution. Figure 7-9 shows a traverseline 520.16 feet long bearing S61°25'E. To determinethe latitude, you solve the triangle ABC for the lengthof the side AC. From the bearing, you know that the sizeof angle CAB (the angle of bearing) is 61°25'. Thetriangle is a right triangle; thereforeAC = 520.16 cos 61°25' = 248.86 ft.The latitude of a traverse line, then, equals theproduct of the length of the line times the cosine of theangle of bearing.To determine the departure, you solve the trianglefor 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 timestwine of angle of bearing.Figure 7-10.—Departure equals length of traverse line timessine of angle of bearing.The departure of a traverse line, then, equals thelength of the line times the sine of the angle of bearing.The latitude of a traverse line is designated north orsouth and the departure is designated east or westfollowing the compass direction of the bearing of theline. A line bearing northeast, for example, has a northlatitude and east departure. In computations, northlatitudes are designated plus and south latitudes minus;east departures are designated plus and west departuresminus.7-9
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