1. **State the problem:** We have a right triangle with one leg of length 40, an angle adjacent to this leg of 22°, and the hypotenuse labeled as $x$. We want to find the length of the hypotenuse $x$. 2. **Identify the formula:** In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 22^\circ$, the adjacent side is 40, and the hypotenuse is $x$. So, $$\cos(22^\circ) = \frac{40}{x}$$ 4. **Solve for $x$:** Multiply both sides by $x$ and then divide both sides by $\cos(22^\circ)$: $$x \cdot \cos(22^\circ) = 40$$ $$\cancel{x} \cdot \cos(22^\circ) = 40 \Rightarrow x = \frac{40}{\cos(22^\circ)}$$ 5. **Calculate the value:** Using a calculator, $$\cos(22^\circ) \approx 0.9272$$ $$x = \frac{40}{0.9272} \approx 43.14$$ 6. **Conclusion:** The length of the hypotenuse $x$ is approximately 43.14 units.