The above diagram shows a typical case of solving a triangle when we are given two sides and one non-included angle.
Here, we are given side b, side a and its opposing angle A.

The number of solutions we will get depends upon the length of side a compared to the height, which is determined by this formula:

• side a < height - no solution because side a doesn't "reach" side c.



• side a = height - one solution.
Side a just "reaches" side c and forms a right triangle.



• side a > height - two solutions.
This is the ambiguous case. Side a is long enough to reach side c in two places.
For this to occur, side a has to be greater than the height but less than side c.



• side a >= side b - one solution.
Side a is now so long that it can only intersect the triangle at point B.
Unlike the ambiguous case, there can't be a matching "left side" (like side a prime) because side a is so long, it can no longer intersect the left-side of side c.

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