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# DM42S/Free42/HP 42S: Hyperbolic Triangles: Law of Sines and Cosines

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

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