1. **State the problem:** We have a right triangle POQ with a right angle at P, angle $\angle O = 53^\circ$, opposite side to $\angle O$ is $PQ = 1.8$, and adjacent side to $\angle O$ is $x$. We need to find $x$. 2. **Identify the trigonometric function:** Since $x$ is adjacent to angle $O$ and 1.8 is opposite, we use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Write the equation:** $$\tan(53^\circ) = \frac{1.8}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$: $$x \tan(53^\circ) = 1.8$$ Divide both sides by $\tan(53^\circ)$: $$x = \frac{1.8}{\tan(53^\circ)}$$ 5. **Calculate $\tan(53^\circ)$:** $$\tan(53^\circ) \approx 1.3270$$ 6. **Substitute and simplify:** $$x = \frac{1.8}{1.3270}$$ 7. **Final calculation:** $$x \approx 1.356$$ 8. **Round to the nearest tenth:** $$x \approx 1.4$$ **Answer:** $x \approx 1.4$