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Determining Lat, Long using trigonometry

  1. Mar 15, 2012 #1
    I am not sure if this is entirely possible, as my spherical trig skills are lacking.

    Would it be possible to determine the Lat and Long coordinates for a position on the Earth knowing the following.

    1. True North Pole is at 90°N
    2. Geomagnetic North Pole is at 82.7°N, 114.4°W
    3. Knowing the direction of True North, I can determine the angle separating the two at my position.

    The vertices of the spherical triangle would be.
    1. Point A would be the True North Pole.
    2. Point B would be the Geomagnetic North Pole.
    3. Point C would be my location.

    The sides of the spherical triangle would be.
    1. Line AB, or γ
    2. Line BC, or α
    3. Line AC, or β

    Side γ has a known length, the distance from the True Pole to GM Pole, which is 820.76km. With Earth's radius at 6371km, this works out to be 0.13 radians, or 7.38°.

    [itex]sin C/sin γ = -1.07703 = sin A/sin α = sin B/sin β[/itex] Correct?

    Seems to me the other lengths should be able to be determined, and then perhaps the coordinates of Point C. Is that possible?
  2. jcsd
  3. Mar 16, 2012 #2


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  4. Mar 16, 2012 #3
    Maybe I have the law of sines upside down?

    C is the angle between vertices, γ is the length of the opposite side in degrees, so then

    sin γ/sin C = -0.92848

    I know the lat, long of two vertices, A and B, of the triangle, and the length of one side γ, and the angle of its opposite vertice C.
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