Law of Cosine & SAS Area of Triangle Advanced Example

I work through a fun problem working with the area of a triangle to find some information about the angle included between two given sides. We then use the Law of Cosine to find the unknown side of this non right triangle.
Part 1) Working with the area of a triangle SAS formula (1/2)absinC and a given area we find some information about the included angle 0:55
Part 2) Using a Pythagorean Identity and the Law of Cosine we find two possible measurements of the third side of this triangle. 4:30

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