Reg, G4FGQ wrote:
"It`s purely a matter of Spherical Geometry."
The ARRL agrees with Reg. The 19th edition of the ARRL Antenna Book on
page 23-24 gives path distance versus vertical wave angle for a one-hop
transmission using the F2 layer in Fig 23. Of course these are only
based on a variable reflecting layer height.

For 500 miles, 40 to 70 degrees.

For 1000 miles, 20 to 35 degrees.

For 1500 miles, 10 to 22 degrees.

For 2000 miles, 4 to 15 degrees.

For 2500 miles, less than 8 degrees.

Neither elevation nor azimuth angles are exact as the wave is subject to
detours but it helps to have an idea of the usual best angles.

Best regards, Richard Harrison, KB5WZI