Answer
$BC=5.2$.
$AC=24.5$.
Work Step by Step
The given values are
$AB=25$ and $\angle A=12^{\circ}$.
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.
$\Rightarrow 25\cdot \sin (12^{\circ}) =BC$
Simplify.
$\Rightarrow 5.2=BC$.
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.
$\Rightarrow 25\cdot \cos (12^{\circ}) =AC$
Simplify.
$\Rightarrow 24.5=AC$.
