Answer
$BC=6.7$.
$AC=9.9$.
Work Step by Step
The given values are
$AB=12$ and $\angle A=34^{\circ}$.
The triangle is shown in the image file.
Use trigonometric ratios.
$\Rightarrow \sin A =\frac{BC}{AB}$
Multiply both sides by $AB$.
$\Rightarrow AB\cdot \sin A =AB\cdot \frac{BC}{AB}$
Simplify.
$\Rightarrow AB\cdot \sin A =BC$
Substitute all values.
$\Rightarrow 12\cdot \sin (34^{\circ}) =BC$
Simplify.
$6.7 =BC$.
Now use
$\Rightarrow \cos A =\frac{AC}{AB}$
Multiply both sides by $AB$.
$\Rightarrow AB\cdot \cos A =AB\cdot \frac{AC}{AB}$
Simplify.
$\Rightarrow AB\cdot \cos A =AC$
Substitute all values.
$\Rightarrow 12\cdot \cos (34^{\circ}) =AC$
Simplify.
$9.9=AC$.
