Just come across a part of a core mathematics trigonometry problem today morning, I and my student used different ways to solve it, but actually, same results turn up:
find in terms of .
(Note: this is an ‘A.S.S.’ given, but the triangle can be uniquely determined.)
Method 1 (cosine law)
It is easy to show , hence
Method 2 (sine law)
( is rejected)
Of course, values of are concretely given in that core math question.