In the case of a triangle, it is relatively easy to find the three internal angles given the lengths of the three sides by applying the cosine rule. Is it similarly possible to find the angles of a simple (non-self-intersecting) quadrilateral given the lengths of the four sides?
Sub-questions:
- Are there possibly multiple solutions to a given set of parameters in this case?
- If it is not possible to solve in general, is it at least possible to solve the problem given the constraint that the quadrilateral is convex?
- How to determine the solution(s)?
Thank you!