# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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My \$.02 on Az
From: Gordon Talge
Date: 1998 Aug 18, 5:01 PM

```I use the formulae in the "Sight Reduction Procedures" in the Nautical
Almanac.

They have:

S = sin Dec
C = cos Dec cos LHA
Hc = invsin(S sin Lat + C cos Lat )

and

X = ( S cos Lat - C sin Lat ) / cos Lat

If X > +1 set X = +1
IF X < -1 set X = -1

A = invcos X

If LHA > 180 then Z = A
Otherwise Z = 360 - A.

This seems to work just fine.

There are probably several formulae to find the Z. In the past
certain formulae were used because they worked easier with log trig
tables or perhaps sliderules.

For example: A plane oblique triangle. Let a = 49.50, b = 30.26,
and C = 44degs 39 mins. Solve for side c.

Well this begs for the Law of Cosines: c^2 = a^2 + b^2 - 2ab cos C.
The book I have "Trigonometry for Navigating Officers" by Winter
circa 1928 England says to use the Tangent Formula :

tan ((A-B)/2) = (a-b)/(a+b) tan((A+B)/2) or some variation of this
formula. They also of course use logs and tables.

Well I am sure using logs and tables this formula is easier and better,
using a pocket calculator the Law of Cosines is much much easier.

-- Gordon

,,,
(. .)
+-----------------------ooO-(_)-Ooo----------------------+
|  Gordon Talge WB6YKK            e-mail: gtalge@pe.net  |
|  Department of Mathematics      QTH: Loma Linda, CA    |
|  Notre Dame High School         Lat.  N  34� 03.1'     |
|  Riverside, CA 92506            Long. W 117� 15.2'     |
|  http://www.pe.net/ND                                  |
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