1. **State the problem:** We have a right triangle with an angle of $53^\circ$ at vertex O, the side adjacent to this angle is 1.8, and the side opposite this angle is $x$. We need to solve for $x$. 2. **Identify the trigonometric function:** Since $x$ is opposite the angle and 1.8 is adjacent, we use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Write the equation:** $$\tan(53^\circ) = \frac{x}{1.8}$$ 4. **Solve for $x$:** Multiply both sides by 1.8: $$x = 1.8 \times \tan(53^\circ)$$ 5. **Calculate the value:** $$x = 1.8 \times 1.3270 = 2.3886$$ 6. **Round to the nearest tenth:** $$x \approx 2.4$$ **Final answer:** $x \approx 2.4$