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That sounds like too much work, there's a specific table for this: Bowditch, Table-17

https://campus.sailoog.com/mod/url/view.php?id=373&lang=en

Here's some links to the math.

https://besjournals.onlinelibrary.wiley.com/doi/full/10.1046/j.1365-2664.2001.00615.x

https://hrcak.srce.hr/file/148120

Range from calculated dip of the shore horizon
From: David Pike
Date: 2018 Oct 4, 13:32 -0700

That took a bit of figuring out.  Are you saying that you add the angle between the object’s waterline and the sea horizon behind it to the dip of the sea horizon?  That would give you the dip of the waterline of the object.  Then go into the “DIP OF THE SHORE HORIZON or Dip at Different Ranges” table (P519 in my 1991 copy of Nories).  Go vertically down from height of eye. Then when you get to the calculated dip of the waterline of the object, go left to get range.  As you say, for a height of eye of 5ft, as might be encountered in a cruising yacht, it doesn’t look particularly useful.  However, for a pole sticking out of the sea, there is the advantage that the range calculated doesn’t seem to be affected by the height of the tide.  DaveP