The law of sines works closely with the law of cosines. In order to solve a problem surveyors often use both starting with the law of cosines and switching to the law of sines to finish the computation.

Here is an example of how this might be utilized:

Based on the givens, the Law of Sines can be used to find either other sides or other angles!

The next step:

It\’s a negative latitude because the bearing is south. It\’s a positive departure because the bearing is east. We are now ready to calculate the coordinates for point C. Northing point A 10,000 – 2217.50 = Northing point C 7782.50. Easting point A 10,000 + 2037.90 = 12037.90.

You should check your work by calculating side CB and calculating the change in latitude and departure from point C to point B. Did you match the given coordinates for point B when you did so? This is referred to as \”checking in\”.

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See also: Law of Cosines, Side-Angle-Side (SAS) and Law of Cosines, Side-Side-Side (SSS)