(42S) Hyperbolic Triangles: Law of Sines and Cosines
07-26-2019, 02:00 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,202 Joined: Dec 2013
(42S) Hyperbolic Triangles: Law of Sines and Cosines
Blog Entry: http://edspi31415.blogspot.com/2019/07/d...ngles.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 END

HYPANG: 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 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
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