(First draft?)

Formulas:

sin A / sin a = sin B / sin b = sin C / sin c

cos A = - cos B cos C + sin B sin C cos a

cos a = cos b cos c + sin b sin c cos A

A, B, C are angles formed by the great circles (the "lines" of the Spherical triangle). Note that A + B + C > 180°. a, b, and c measure the arc length of great circles as angles measured from the center of the sphere.

Source: http://www.krysstal.com/sphertrig.html

Program: Label S

Calculator: HP 35S

I am not sure if I covered all possible scenarios.

Memory registers B and C are used for temporary purposes.

Given: B, A, b; Goal: a; Label S001

S001 LBL S

S002 SIN

S003 x<>y

S004 SIN

S005 ÷

S006 x<>y

S007 SIN

S008 ×

S009 ASIN

S010 RTN

Given: b, a, B; Goal: A; Label S011

S011 SIN

S012 x<>y

S013 SIN

S014 ×

S015 x<>y

S016 SIN

S017 ÷

S018 ASIN

S019 RTN

Given: a, b, c; Goal: A; Label S020

S020 STO C

S021 COS

S022 x<>y

S023 STO B

S024 COS

S025 ×

S026 x<>y

S027 COS

S028 x<>y

S029 -

S030 RCL B

S031 SIN

S032 RCL C

S033 SIN

S034 ×

S035 ÷

S036 ACOS

S037 RTN

Given: b, A, c; Goal: a; Label S038

S038 STO C

S039 SIN

S040 x<>y

S041 COS

S042 ×

S043 x<>y

S044 STO B

S045 SIN

S046 ×

S047 RCL C

S048 COS

S049 RCL B

S050 COS

S051 ×

S052 +

S053 ACOS

S054 RTN

Given: A, B, C; Find: a; Label S055

S055 STO C

S056 COS

S057 x<>y

S058 STO B

S059 COS

S060 ×

S061 x<>y

S062 COS

S063 +

S064 RCL B

S065 SIN

S066 RCL C

S067 SIN

S068 ×

S069 ÷

S070 ACOS

S071 RTN

Examples:

Given: B = 3.2145°, A = 2.2718°, b = 40°; XEQ S001; Result: a ≈ 65.4058°

Given: b = 60°, a = 40°, B = 4.95°; XEQ S011; Result A ≈ 3.6720°

Given: a = 4.11°, b = 5°, c = 6.03°; XEQ S020; Result A ≈ 42.5439°

Given: b = 3.996°, A = 49°, c = 6.314°; XEQ S038; Result a ≈ 4.7636°

Given: A = 124°, B = 45°, C = 76°; XEQ S055; Result a ≈ 124.4509°

Enjoy - hope this helps and have a great day!

Eddie

This blog is property of Edward Shore. 2013