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A straight line from A (53°S 155°E) to B (53°S 170°W) is drawn on a Lambert Conformal conical chart with standard parallels at 50°S and 56°S. When passing 175°W, the True Track is…

  • A
    258.0°
  • B
    282.0°
  • C
    080.0°
  • D
    102.0°

Refer to figure.
Lambert chart: Convergency = Change of longitude º x Convergence factor

Where convergence factor equals sin of Parallel of Origin.

Parallel of Origin: half way between standard parallels - in this case, standard parallels 50ºS and 56ºS => Parallel of origin is 53ºS

Convergence factor = Sin 53º = 0.7986

  • Both points are on latitude 53ºS. Therefore, RLT = 090ºT
  • Difference between RLT and GCT = Conversion Angle

First Step: Calculate GCT at B (from RLT at B and Conversion Angle)

At B
Conversion angle = 1/2 change of longitude x convergence factor

= 1/2 (35º) x 0.7986 = 13.98° (approx. 14°)

GCT at B = RLT - Conversion angle = 090° - 014° = 076°

Second Step: using convergency, use GCT at B to calculate GCT at 175°W

Convergency = change of longitude x convergence factor

= 5° x 0.7986 = 4°

  • GCT at 175ºW > GCT at B
  • At 175ºW = GCT at B + Convergency

GCT = 076° + 004° = 080°

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