**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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