Triangles !

Couldn't you just use the law of sines?

Using the Sine Rule,

\(\frac{16}{sin(54)}=\frac{12}{sin C}\)

\(12sin(54)=16sinC\)

\(sinC=\frac{3sin54}{4}\)

\(C = sin{}^{-1}(\frac{3sin54}{4})\)which is about 37.35579 degrees

54 + 37.35579...... + A = 180  (angle sum of triangle)

                                 A = 88.6442......

Applying the Sine Rule again,

\(\frac{a}{sin A}=\frac{16}{sin54}\)

\(a = \frac{16sin88.6442......}{sin54}=19.77155\)