Answer
$AB=26.9$.
$AC=20.0$.
Work Step by Step
The given values are
$BC=18$ and $\angle A=42^{\circ}$.
The triangle is shown in the image file.
Use trigonometric ratios.
$\Rightarrow \sin A =\frac{BC}{AB}$
Multiply both sides by $\frac{AB}{\sin A}$.
$\Rightarrow \frac{AB}{\sin A}\cdot \sin A =\frac{AB}{\sin A}\cdot\frac{BC}{AB}$
Simplify.
$\Rightarrow AB=\frac{BC}{\sin A}$
Substitute all values.
$\Rightarrow AB=\frac{18}{\sin 42^{\circ}}$
Simplify.
$AB=26.9$.
Now use
$\Rightarrow \tan A =\frac{BC}{AC}$
Multiply both sides by $\frac{AC}{\tan A}$.
$\Rightarrow \frac{AC}{\tan A} \cdot \tan A =\frac{AC}{\tan A} \cdot \frac{BC}{AC}$
Simplify.
$\Rightarrow AC =\frac{BC}{\tan A}$
Substitute all values.
$\Rightarrow AC =\frac{18}{\tan 42^{\circ}}$
Simplify.
$AC=20.0$.
