1. **State the problem:** We have two flying discs detected at the same angle of elevation $39.48^\circ$ but at different distances from the receiver: 826 m and 1296 m. We need to find the difference in their heights. 2. **Formula used:** The height $h$ of an object at distance $d$ and angle of elevation $\theta$ is given by: $$h = d \times \sin(\theta)$$ 3. **Calculate the height of the first disc:** $$h_1 = 826 \times \sin(39.48^\circ)$$ 4. **Calculate the height of the second disc:** $$h_2 = 1296 \times \sin(39.48^\circ)$$ 5. **Calculate the difference in height:** $$\Delta h = h_2 - h_1 = (1296 - 826) \times \sin(39.48^\circ)$$ 6. **Evaluate the sine:** $$\sin(39.48^\circ) \approx 0.636$$ 7. **Calculate the difference:** $$\Delta h = 470 \times 0.636 = 298.92$$ 8. **Round to the nearest metre:** $$\boxed{299 \text{ metres}}$$ The difference in height between the two discs is approximately 299 metres.