1. **State the problem:** We have a right triangle with angles 70° and 30°, and the hypotenuse length is 5. We need to find the length of side $x$ adjacent to the 30° angle. 2. **Recall the relevant formula:** In a right triangle, the side adjacent to an angle $\theta$ can be found using the cosine function: $$x = \text{hypotenuse} \times \cos(\theta)$$ 3. **Apply the formula:** Here, $\theta = 30^\circ$ and hypotenuse = 5, so $$x = 5 \times \cos(30^\circ)$$ 4. **Calculate $\cos(30^\circ)$:** $$\cos(30^\circ) = \frac{\sqrt{3}}{2}$$ 5. **Substitute and simplify:** $$x = 5 \times \frac{\sqrt{3}}{2} = \frac{5\sqrt{3}}{2}$$ 6. **Final answer:** $$x = \frac{5\sqrt{3}}{2} \approx 4.33$$ This means the side $x$ adjacent to the 30° angle is approximately 4.33 units long.