1. **State the problem:** We have a right triangle with a right angle at vertex P. The side opposite the 23° angle (at vertex O) is 43 units, and we want to find the length of side $x$ adjacent to the 23° angle. 2. **Identify the trigonometric function:** Since we know the side opposite the angle and want the adjacent side, we use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Write the equation:** $$\tan(23^\circ) = \frac{43}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and then divide both sides by $\tan(23^\circ)$: $$x \cdot \tan(23^\circ) = 43$$ $$x = \frac{43}{\tan(23^\circ)}$$ Intermediate step showing cancellation: $$x = \frac{43}{\cancel{\tan(23^\circ)}} \cdot \cancel{\frac{1}{\tan(23^\circ)}}$$ 5. **Calculate the value:** $$\tan(23^\circ) \approx 0.4245$$ $$x \approx \frac{43}{0.4245} \approx 101.3$$ 6. **Final answer:** The length of side $x$ is approximately **101.3** units.