Answer
$10.7 \ cm$
Work Step by Step
Using the definition of tangent of the angle A, we have
$$
\tan A=\tan 34.2=\frac{length \ of \ side\ opposite\ angle\ A}{length \ of \ side\ adjacent\ angle\ A}=\frac{a}{15.8}
.$$
That is,
$$
a= 15.8\times \tan 34.2 =10.7 \ cm
.$$
