(42S) Hyperbolic Triangles: Law of Sines and Cosines - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: General Software Library (/forum-13.html) +--- Thread: (42S) Hyperbolic Triangles: Law of Sines and Cosines (/thread-13340.html) (42S) Hyperbolic Triangles: Law of Sines and Cosines - Eddie W. Shore - 07-26-2019 02:00 PM Blog Entry: http://edspi31415.blogspot.com/2019/07/dm42sfree42hp-42s-hyperbolic-triangles.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