Answer
$a\approx6.9$ in.
$b\approx9.8$ in.
Work Step by Step
$\sin35^{\circ}=\frac{a}{12}$
$a=12\times\sin35^{\circ}$
$a\approx6.9$
Using Pythagorean Theorem to find $b$.
$b=\sqrt {12^{2}-a^{2}}$
$b\approx\sqrt{12^{2}-6.9^{2}}$
$b\approx9.8$