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(42S) Hyperbolic Triangles: Law of Sines and Cosines - Eddie W. Shore - 07-26-2019 02:00 PM
Blog Entry: http://edspi31415.blogspot.com/2019/07/dm42sfree42hp-42s-hyperbolic-triangles.html
There are three solvers:
HYPSIN: Law of Sines - Hyperbolic Triangles
sinh SA / sin ∠A = sinh SB / sin ∠B = sinh SC / sin ∠ C
The solver uses sinh SA / sin ∠A = sinh SB / sin ∠B . Use the clever use of the labels is needed with the solver.
HYPANG: Law of Cosines - Angle Dominant - Hyperbolic Triangles
cos ∠A = - cos ∠B * cos ∠C + sin ∠B * sin ∠C * cosh SA
HYPSDE: Law of Cosines - Side Dominant - Hyperbolic Triangles
cosh SA = cosh SB * cosh SC - sinh SB * sinh SC * cos ∠A
HP 42S/DM42/Free 42 Solver Programs
HYPSIN: Law of Sines - Hyperbolic Triangles
Code:
00 { 51-Byte Prgm }
01▸LBL "HYPSIN"
02 MVAR "SA"
03 MVAR "∡A"
04 MVAR "SB"
05 MVAR "∡B"
06 RCL "SA"
07 SINH
08 RCL "∡A"
09 SIN
10 ÷
11 RCL "SB"
12 SINH
13 RCL "∡B"
14 SIN
15 ÷
16 -
17 ENDHYPANG: Law of Cosines - Angle Dominant - Hyperbolic Triangles
Code:
00 { 63-Byte Prgm }
01▸LBL "HYPANG"
02 MVAR "∡A"
03 MVAR "∡B"
04 MVAR "∡C"
05 MVAR "SA"
06 RCL "∡B"
07 COS
08 +/-
09 RCL "∡C"
10 COS
11 ×
12 RCL "∡B"
13 SIN
14 RCL "∡C"
15 SIN
16 ×
17 RCL "SA"
18 COSH
19 ×
20 +
21 RCL "∡A"
22 COS
23 -
24 .END.HYPSDE: Law of Cosines - Side Dominant - Hyperbolic Triangles
Code:
00 { 66-Byte Prgm }
01▸LBL "HYPSDE"
02 MVAR "SA"
03 MVAR "SB"
04 MVAR "SC"
05 MVAR "∡A"
06 RCL "SB"
07 COSH
08 RCL "SC"
09 COSH
10 ×
11 RCL "SB"
12 SINH
13 RCL "SC"
14 SINH
15 ×
16 RCL "∡A"
17 COS
18 ×
19 -
20 RCL "SA"
21 COSH
22 -
23 ENDExamples
Degrees mode is used
Example 1
Step 1: Solve for Z, use HYPSDE:
23° -> ∠A
1.766 -> SB
1.8 -> SC
Solve for SA: 1.0969
Step 2: Solve for X°, use HYPSIN:
1.8 -> SA
23° -> ∠A
1.766 -> SB
Solve for ∠B: 22.1432°
Step 3: Solve for Y°, use HYPSIN:
1.8 -> SA
23° -> ∠A
1.0969 -> SB
Solve for ∠B: 10.1773°
Example 2
Step 1: Solve for Z°, use HYPANG
40° -> ∠A
42° -> ∠B
1.365 -> SA
Solve for ∠C: 57.0139°
Step 2: Solve for X, use HYPSIN
40° -> ∠A
42° -> ∠B
1.365 -> SA
Solve for SB: 1.4004
Step 3: Solve for Y, use HYPSIN
40° -> ∠A
57.10739° -> ∠B
1.365 -> SA
Solve for SB: 1.6050
Sources:
Martin, Angel "Hyperbolic Triangles for the HP-41" http://hp41programs.yolasite.com/hyperbolictriangle.php Retrieved May 15, 2019
Wikipedia "Hyperbolic Triangles" Last edited May 29, 2019. https://en.wikipedia.org/wiki/Hyperbolic_triangle Retrieved June 9, 2019