__To Calculate a Side - The Cosine Formula__
Cos(a) = Cos(b) x Cos(c) + Sin(b) x Sin(c) x Cos(A) Applying this to the PZX triangle we get:- Cos(Zenith Distance) = Cos(co-Lat) x Cos(co-Dec) + Sin(co-Lat) x Sin(Co-Dec) x Cos(LHA) Because Sin(co-A) = Cos(A) and Cos(co-A) = Sin(A) Cos(Zenith Distance) = Sin(Lat) x Sin(Dec) + Cos(Lat) x Cos(Dec) x Cos(LHA) If Altitude is preferred; Zenith Distance = co-Altitude thus Sin(Altitude) = Sin(Lat) x Sin(Dec) + Cos(Lat) x Cos(Dec) x Cos(LHA) __For an Angle__
Tan(C) = Sin(A)/ [Sin(b)/ Tan(c) – Cos(b) x Cos(A)] Inserting terms from the PZX triangle this becomes Tan(Az) = Sin(LHA)/ [Sin(co-Lat)/ Tan(co-Dec) – Cos(co-Lat) x Cos(LHA)] Or Tan(Az) = Sin(LHA)/ (Cos(Lat) x Tan(Dec) – Sin(Lat) x Cos(LHA)) __The Spherical Sine Formulae__
Sin(a)/ Sin(A) = Sin(b)/ Sin(B) = Sin(c)/ Sin(C) |