How does the radiation pattern of a horizontally-polarized antenna mounted above a long slope compare with the same antenna mounted above flat ground?
Why The elevation pattern of a horizontal antenna is set largely by reflections from the ground beneath it, and the lobe forms relative to that reflecting surface. When the ground slopes away, the whole reflection geometry tilts downward, so the main lobe is aimed lower with respect to the true horizon in the downhill direction. A lower takeoff angle is exactly what favors long-haul DX, which is why hilltop stations with a clear downhill slope work so well.
Watch out The choice saying the takeoff angle increases has the tilt backwards: that is what happens looking uphill, where the rising ground pushes the lobe up. The beamwidth answers confuse the vertical pattern effect with horizontal azimuth beamwidth, which is set by the antenna itself, not the slope.
Slope tilts the ground mirror: downhill means the lobe points down, lower takeoff angle, better DX.