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?