Appendix J a = sin H Cos 12 b = Sin A2 Cos 1 - Cos H Sin, BI Cos R2 H = 180 ¡Sin I COs B1 COs B2 + L TT x = Y/ (F+F2) - AF2 20X 103+242 + 1922 (a8-54+4412 cot 1804) Compute A21 in degrees (Azimuth P2 to P1) if L =0 A21 = V + 180° if I >0 Where:
180° + Arc Ian & if Arc Ian ₫ < 0 V = Arc Ian a if Arc Tan = O c = Sin H Cos 11 d = sin B2 Cos ß1 Cos H - sin B1 Cos A2 Par 2 Page 3
AC 90-45A 2/21/75 Appendix J Computation of the Geodetic Description of a True Bearing and Distance From A Given Geodetic Point.
Given: B1 Geodesic Latitude of a P1 L1 Geodesic Longitude of a P1 S Geodesic Length A12 Azimuth of Geodesic from Pı to Pz And:
F = 3.3901 X 10-3 Ao = 3443.95594 Required: B2 Geodesic Latitude of P2 L2 Geodesic Longitude of P2 A21 Azimuth of Geodesic from Pz to PI Compute B, Geodesic Latitude B2 = Arc Tan Tan 132] Where:
Sin B1 Cos D + Cos B1 COs A12 Sin P B2 = [cos? Bo + (cos Acos By cos A12 - Sin By Sin D)Z] IZ D = x 90482 sin r - M82 (2r - 180 sin 2x) + 27} 4332 Sin 2r + 3 (228 - 22f0 sin 2r - 16r 03 x + 1809 cos + Sin 2r) A1 = h Si? By Cos I + Cos ß1 COS A12 Sin B1 Sin r T = 180S TT (1-F)AO Page 4 Par 2
Appendix J M, = h (1 - cos Bo 1 = 1 + sin B B1 = Arc Tan [ (1-F) Tan B1] cos So = Cos A1 Sin A12 E, = (1-F) *2 -1 Compute Lz (Geodesic Longitude) [2 - 360 52 18 21 > 180 1521 12 = = 180 Líz = 41 - V Cos Bo - Ić = 270 A1F2 Sin r - Fr + 3M, F2 4 - (r - 20 Sin 2t) Ic - 180 if Sin P ≥ 0 and Sin A12 < 0 Ic + 180 if Sin < O and Sin A12 ≥ 0 Lc =
- 360 if Sin O = 0 and Sin A12 = 0 Otherwise Ic = Arc Tan cos B1 Cos O - Sin B1 Sin D Cos A12 Sin A Sin A12 - where -90 = 1c = 90 Compute Geodesic Azimuth A21 in degrees (Áź1 + 180°) if Sin A12 = 0 A21 = A21 if Sin A12 = 0 Par 2 Page 5
Appendix J A + 180° i£ < O Aź1 = ifĂ≥o À = Arc Ian 5 where -90° = À ≤ 90° (Principle Arc Tan) N = cos Bo D = Cos B1 cos A12 Cos D - sin 11 sin D Page 6 Par 2