If the body observed by a navigator is on the prime vertical, the astronomical triangle is right-angled at the zenith, and the solution of the triangle is about one-fourth as hard as is the solution of the general triangle. Yet we find this fact blithely ignored; and we find a much more difficult solution adopted in the name of universality. It is as though a man, because he puts 2.12X1.95 on the slide rule, should also put 2.00X2.00 on the rule.
Astronomical triangle, declination same name as latitude:
Applying the sine rule—
cosh/sint = cosd/sinZ
cosh = sint cosd/sinZ
And when Z = 90°
cos h = sin 2 cos d
Let us apply this to Problem I of H. O. publication 211, where we are told that the body is on the prime vertical.
Which answer is more nearly correct (36°-01.58r by 6-place tables) than the 36°-01.5' got with greater trouble by the H. O. 211 method.