I think the answer lies in the definition of cosine:
cos θ = (X / r)
Where:
θ = angle in degrees
X = adjacent side of triangle contained within the unit circle
r = 1, radius of the unit circle
Since we are using the unit circle where r = 1:
cos θ = X
The formula states: A = cos [(P^2+R^2-L^2)/2PR]
If you consider the formula for the inverse cosine, cos^-1, it states:
cos^-1 X = θ
If the formula is written: A = cos^-1 [(P^2+R^2-L^2)/2PR], the math works out.
cos^-1 (8404/8880) = 18.8