1. **Stating the problem:** We have a right-angled triangle with one angle of 64° and hypotenuse length 52. We need to find the length of side $m$ adjacent to the 64° angle. 2. **Formula used:** In a right triangle, the adjacent side to an angle is found using the cosine function: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ 3. **Apply the formula:** Here, $\theta = 64^\circ$, hypotenuse = 52, and adjacent side = $m$. $$\cos(64^\circ) = \frac{m}{52}$$ 4. **Solve for $m$:** $$m = 52 \times \cos(64^\circ)$$ 5. **Calculate the cosine:** $$\cos(64^\circ) \approx 0.4384$$ 6. **Find $m$:** $$m = 52 \times 0.4384 = 22.7968$$ 7. **Round to 1 decimal place:** $$m \approx 22.8$$ **Final answer:** $m = 22.8$