DM42S/Free42/HP 42S: Hyperbolic Triangles: Law of Sines and Cosines
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
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 END
HYPANG: Law of Cosines - Angle Dominant - Hyperbolic Triangles
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
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 END
Examples
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
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
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
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 END
HYPANG: Law of Cosines - Angle Dominant - Hyperbolic Triangles
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
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 END
Examples
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
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
