Posted by John  PLEASE Help! on Monday, April 11, 2011 at 1:36am.
After shooting the trailing edge of the Sun on 11 April 2008, the observed clockwise angle from the mark to the edge of the sun is 259 degrees 44 minutes 51 seconds, the latitude is 32 degrees 47 minutes 54 seconds North, the longitude is 079 degrees57minutes 38 seconds, the time is 11 hours 17 minutes  30 seconds Daylight Savings time. The LaPlace correction is 3seconds. Determine the geodetic bearing to the mark.

Geomatics  MathMate, Monday, April 11, 2011 at 8:58am
Briefly, you will need access to the Nautical Almanac, published jointly by UK and US yearly. Some free versions are available on the web for past years.
The nautical almanac gives the position of the sun (and many other celestial bodies) in longitude and latitude at any hour of the year.
Most of the time, this, together with the time of the day, is used to calculate the position of the observer. In your case, the observer's position is known, so is that of the sun. So you can calculate the observed bearing of the sun using spherical trigonometry, and hence that of the mark.
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