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,

$\frac{a}{sin A}=\frac{16}{sin54}$

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