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Re: A triangle on the equator
From: Lars Bergman
Date: 2025 Oct 6, 13:44 -0700
From: Lars Bergman
Date: 2025 Oct 6, 13:44 -0700
Frank,
It is not an exact 3:4:5 triangle. Using Vincenty's formula, and WGS84, I get
AB = 11057.4 m (5.97 M, where 1 M = 1852 m)
BC = 14842.6 m (8.01 M)
AC = 18508.6 m (9.99 M)
and an initial great circle course of 53°18.9'
Regarding meridional parts, there is one rather simple formula: M(lat) = artanh(sin(lat)) - e·artanh(e·sin(lat)), where e is the eccentricity and the result will be in radians. Then, M(6') = 1.733646 mrad = 5.96'. And M(0) = 0. Dividing difference in longitude by difference in meridional parts gives tan course = 1.3423, and the rhumb line course 53°18.9', equal to the great circle course above.
Whether WGS84 is a reasonably good model for this specific part of the earth, or not, I have no idea.
Lars
