1. **Problem:** Find the side length $x$ in triangle ABC with right angle at C, $AB=16$, angle at B is $32^\circ$, and side $AC=x$. 2. **Formula and rules:** In a right triangle, sides and angles relate by trigonometric ratios. Here, angle $B$ is adjacent to side $AC$ and opposite to side $BC$. The hypotenuse is $AB$. 3. Use cosine for adjacent side: $$\cos(32^\circ) = \frac{AC}{AB} = \frac{x}{16}$$ 4. Solve for $x$: $$x = 16 \times \cos(32^\circ)$$ 5. Calculate: $$x = 16 \times 0.8480 = 13.57$$ 6. **Answer:** $x \approx 13.57$ (rounded to nearest hundredth).