## Sunday, June 2, 2013

### HP 35S: Spherical Triangle

(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

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