No need to concentrate on how tall. Concentrate on the angle that both objects would be at from a level sight.

Draw it if you think you can.

Yes, that is something you need to do as well.

But the big issue with your diagram isn't so much the size of the object, but just how far apart they are.

Notice that in your diagram, as I already explained, you have a distance of 4300 km, being nice and pretending that is along the surface, rather than a straight line, that would amount to ~40 degrees, or roughly 30 times the maximum angle that could be involved in the situation described in the OP.

For a more representative example, here you go (I couldn't be bothered drawing in the Earth, so instead I just drew in 2 lines, at the appropriate angles):

Note the above, while it does have the angles correct, does suffer from one big flaw, digital images like this have aliasing so you can easily see they tilt in opposite directions. This is very obvious in the middle where it moves over 1 step (1 px), and less so at the ends.

So a better representation would be this:

Now you have a bunch of lines offset by that small angle, such that you can divide them into 2 sets where every line in a set is parallel. Can you pick which ones are which, just using your eyes without using any tools such as paint to measure the tilt?

Oh, and also tell me which set is tilted further to the right vs which set is more vertical.

And all of that is involving the maximum angle. He didn't tell us the distance he actually was when he started to see it, which would likely be a much smaller angle, which would make it even harder.

And of course, with these lines, you are looking at them side on, so it is much easier to see the difference.

What you need is to look at them head on, like this:

Or if you would prefer a more textured version, like this:

From left to right, these are cylinders at various angles to the viewer.

Can you tell which is vertical and which is at various angles? (and what those angles are?)

Just which do you think should correspond to the lighthouse?