**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.

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