1. **State the problem:** Alan is flying at an altitude of 2000 m. The angle of depression to a landmark on the ground is 78°. We need to find the horizontal distance from the airplane to the landmark. 2. **Relevant formula:** In a right triangle, the angle of depression from the airplane corresponds to the angle between the horizontal line from the airplane and the line of sight to the landmark. We can use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ where $\theta = 78^\circ$, opposite side = altitude = 2000 m, and adjacent side = horizontal distance (unknown). 3. **Set up the equation:** $$\tan(78^\circ) = \frac{2000}{d}$$ where $d$ is the horizontal distance. 4. **Solve for $d$:** $$d = \frac{2000}{\tan(78^\circ)}$$ 5. **Calculate $\tan(78^\circ)$:** Using a calculator, $\tan(78^\circ) \approx 4.704$. 6. **Evaluate $d$:** $$d = \frac{2000}{4.704} \approx 425.3$$ 7. **Round to nearest metre:** $$d \approx 425$$ metres. **Final answer:** Alan's horizontal distance to the landmark is approximately 425 metres.