To get the angles using dot product, you need the vectors, not the lengths.
Find:
the dot product of and to get the angle BAC.
the dot product of and to get the angle ABC.
the dot product of and to get the angle ACB.
Use dot products to find all three angles of the triangle.
I already found the lengths of the three sides of the triangle: AB = 3sqrt(2), AC = 3sqrt(6) and BC = 6sqrt(2) and I already know the answers because I found them using trigonometry, but not sure how to do it using dot products.