Why "Two Sides and an Angle" Can Have Two Right Answers
Enter two sides and an angle into a triangle solver, hit solve, and sometimes get back two completely different triangles, both claiming to be correct. That's not a bug. It's a genuine, well-documented feature of the geometry, one trig textbooks call "the ambiguous case" for exactly this reason.
What's actually happening
It only happens with one specific combination: two sides plus an angle that isn't between them (mathematicians call this SSA). Picture building the triangle by hand: draw the known angle, lay the first known side along one of its arms, then swing the second known side from the end of that arm like a compass needle until it reaches the required length. Depending on how long that second side is relative to the angle and the first side, that swinging arm can touch down in two different places, one closer, one farther, both landing at the exact right distance. Each landing point closes off a valid, different triangle that satisfies the same original two sides and angle.
Why the other four combinations never do this
Every other way of giving a triangle three values, three sides (SSS), two sides with the angle between them (SAS), or a side with two angles (ASA or AAS), pins the shape down to exactly one triangle, or none at all if the numbers are geometrically impossible. SSA is the only one where the compass-swing has room to land twice. If a solver ever hands back two answers for a triangle you're building from real measurements, that combination of "two sides, angle not between them" is almost certainly why.
Whether that swing lands once, twice, or not at all comes down to a single comparison: the known angle's own side against the height of the triangle if it were a right angle at that spot. Shorter than that height and the arm never reaches at all, no triangle exists. Exactly that height and it just barely touches, one triangle, a right angle. Longer than that height but still shorter than the other known side, it swings through two valid landing points. Longer than both, back down to one.
What to actually do about it
If the goal is confirming which of the two triangles matches something real, a plot of land, a truss, a part on a drawing, whichever landing point matches an angle or side you can independently measure or already know is the right one; the other is mathematically valid but not the physical answer. If the goal is avoiding the ambiguity entirely, use a different combination when you have the choice: measuring the included angle instead of an adjacent one turns the same problem into SAS, which never splits into two answers. And if the goal is just understanding why a tool returned two rows instead of one, that's the honest, complete answer: both are correct, for two different triangles that happen to share the same three starting numbers.
See it happen directly: enter two sides and a non-included angle into the triangle calculator and it'll show both triangles when there are two.