The equation has two solutions in . One solution in and the other in .
You should better use the cosine rule: find cosine of the other two angles using the sides of triangle and then find the angles.
I have a triangle HPN with two side lengths HP = 54km and HN = 75km and included angle 15 degrees. Let the angles opposite HP and HN be and respectively. By use of the cosine rule I get
Next, I use the sine rule to solve for remaining angles:
The last angle I will find using the sine rule again.
Apprximately, i have a 93 degree triangle here. What did I do wrong?