I'm curious if it is possible to solve completely a triangle given one side and the sum of the other two sides. I'm convinced it's impossible, but wanted to clarify. By solve, I mean find all angles and side lengths.
[Math] Determine triangle given one side and sum of other two sides
geometry
Best Answer
Here's another way to think about it, and it may be more revealing. Geometrically, an ellipse is defined as the locus of all points that have a fixed sum of distances from two fixed foci.
The length of your one fixed side gives you the distance between the foci, and the foci occur at either end of this segment. The third point can occur anywhere along the ellipse defined using the sum of the other two sides. Clearly, an infinite number of triangles can satisfy this requirement.