Let us take the Earth as a perfect sphere.

Place a human on the surface, and let's say he is 1.7m tall. He will be able to see to the horizon, and whatever is nearer than the horizon, but nothing of the Earth's surface beyond it. If we draw a plumbline, a vertical at his location, his sightline to and beyond the horizon will be the green angle H. (EDIT - No, it will not BE the green angle - the sightline and vertical will FORM the angle H)

If there's a ship out there of infinite height, and we also draw a plumb vertical at its location, the angle between that plumb and the vertical we formed at the human's location will be the red angle S

These two lines can only meet (i.e. the human's sightline will meet the ship's infinite height) if angle S is greater than H. If they are equal, the sightline will be parallel to the ship, and can never meet it. If S is less than H, the sightline will diverge away from the ship. The lines can only meet if they converge. If S is greater than H. I could work out the maths to the Nth degree to determine exactly how far, but really ...