Answer
$19.10\ cm$
Work Step by Step
Using the definition of the cosine of angle A, we have
$$
\cos A=\cos 34.2=\frac{length \ of \ side\ adjacent\ angle\ A}{length \ of \ hypotenouse}=\frac{15.8}{c}
.$$
That is,
$$
c=\frac{15.8}{cos 34.2} =19.10\ cm
.$$
