The Law of Sines in a triangle that is SSA, or side-side-angle, meaning we know 2 sides and one angle of the triangle, is an ambiguous case because we can have either one, none, or two answers to the triangle. This is because we only know one definite angle. When we knew at least two definite angles, like in the cases of ASA and AAS, we were able to figure out the third definite angle without wondering if there could be another possible way to draw the triangle. With LIMITED information, it is possible that we can create two different triangles by forming a "bridge" with the side that is given to us for the angle that is not given to us.
After figuring out the value of the angle using the Law of Sines, we use its reference angle to figure out its other possible value. The reference angle is relevant because you can have the angle in the sine quadrant (quadrant II) besides the all quadrant (quadrant I), since it is less than 180 and could be in the boundaries of the Triangle Sum Theorem.
You know there is either no triangle when you hit a "wall" in the beginning or only one triangle when you hit a "wall" after figuring out the first triangle. The "wall" could be something that is not possible like sine x being greater that 1 or less than negative 1 and the angles adding up to something greater than 180 degrees.
The picture below will show you a problem that will give you two answers.
#5 AREA FORMULAS
The pictures below will help you see how the area formulas of a triangle work and how by using either of them you will still get the same answers. This will show you that the law of sines works with working out a triangle that is not a special right triangle.
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