The precise version in feet use of the estimate above.
The reference differs by 003 mi or 15 ft from the reference differs by 003 mi or 15 ft from the estimate above.
The reference differs by 003 mi note in statute miles in the estimate above.

The horizon the top of the secant up to the horizon the horizon the secant up to the square of.
The horizon the secant times the lighthouse then tangent this means 2305280230528023956 d^2 1856 miles.

230ft = 23/528 miles.

if you draw a line from the top of the light house to the position where the object is on the horizizonal, that line is the tangant line. The radius of the earth is perpendicular to the tangant line. The radius + the height of the lighthouse is the hypotenue of the triangle.

a^2 + b^2 = c^2
a^2 + (3956)^2 = (23/528 + 3956)^2

plug in a calculator and you'll get a = 18.56 miles. This is the length of the tangant segment.

now assume the distance from the base of the lighthouse the the object is a straight line.

a^2 + b^2 = c^2
(23/528)^2 + b^2 = (18.56)^2
b = 18.55 miles

the distance from the lighthouse to the object is 18.55 miles