Law of Sines question

Question

sin14°13'36" = sinX

803.94             1879.2

 

X=35°03'44"

 

This seems to be correct, but in the problem that I was doing, it was the complimentary angle of 144°56'12" that was the right one and seem to fit the actual triangle. Why would that be?

 

Thank you,

Jerry

Answer 1

     sin14°13'36"    = sinx

If   --------------       ------    , then sinx = 0.574457652

        803.94           1879.2

 

Since sine is positive in quadrants 1 and 2, there are two possibilities,

  

    x = 35.06° or 144.94°

 

Depending on what other parts of the triangle are known would determine which value of x that would be chosen.  For example, the three angles of the triangle must add up to 180° and the largest side of the triangle must be opposite the largest angle.