1. **Problem statement:** We are given a right triangle EDF with a right angle at E, side ED = 7, and angle F = 49°. We need to find the length of side DF. 2. **Identify the sides:** In triangle EDF, angle E is 90°, so side DF is the hypotenuse, side ED is one leg adjacent to angle F, and side EF is the other leg opposite angle F. 3. **Use trigonometric ratios:** Since we know the adjacent side (ED) and want the hypotenuse (DF), we use the cosine function: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ Here, $\theta = 49^\circ$, adjacent = 7, hypotenuse = DF. 4. **Set up the equation:** $$\cos(49^\circ) = \frac{7}{DF}$$ 5. **Solve for DF:** $$DF = \frac{7}{\cos(49^\circ)}$$ 6. **Calculate the value:** $$DF = \frac{7}{\cos(49^\circ)} \approx \frac{7}{0.6561} \approx 10.67$$ 7. **Round to the nearest tenth:** $$DF \approx 10.7$$ **Final answer:** $$\boxed{10.7}$$