Copyright © 1979-1981 by Steffen Beyer.
This program is free software; you can use, modify and redistribute it under the terms of the GNU General Public License or the GNU Lesser General Public License, as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
It is intended for use e.g. with the TI-58C/59 Calculator Emulator for Android.
Trigonometry
| Triangle Solution | ||||
| α | β | γ | ||
| a | b | c | INIT | CALC |
![[Screenshot]](img/TriangleSolution.png)
Given any(*) three values describing an arbitrary triangle, such as length of side a, length of side b, length of side c, angle α, angle β or angle γ, the program will automatically calculate the missing other three values.
(*): at least one side
In case there is more than one solution (indicated by a blinking 2 after pressing ), press again after viewing the first solution in order to display the values of the second solution.
2nd A' 2nd B' 2nd C' will display 36.86989765, 53.13010235 and 90, respectively.
The program does not interfere with ongoing calculations. None of the functions , , , 2nd A', 2nd B', 2nd C', and uses CLR or = internally.
For example it is possible to enter 2nd A' 2nd B' 2nd C' = in order to make a sanity check that the sum of the angles is indeed 180 degrees (if 2nd Deg is selected).
The program of course also works with 2nd Rad and 2nd Grad.
The program checks the number of arguments and displays a blinking 9.9999999 99 if there are more or less than three arguments, but it does no sanity checks on the arguments themselves in order to see whether the values cannot possibly match a real triangle, such as for example a = 3, b = 11 and α = 19.
In fact the maximum angle α which is possible in this example is easily calculated as 2nd B' 2nd A' which yields 15.82662013.
This example 2nd A' allegedly gives two solutions, the second of which yields negative values - an indication that something is wrong.
When the angle α is smaller than 15.82662013, then there are indeed always two solutions. For example 2nd A' will yield the following two solutions:
a = 3 b = 11 c = 11.57098371 α = 15 β = 71.6230946 γ = 93.3769054 a = 3 b = 11 c = 9.679384465 α = 15 β = 108.3769054 γ = 56.6230946
This program uses registers to and as well as flags and .
α + β + γ = 180 or 2Π or 200
c2 = a2 + b2 - 2ab cos γ
a / sin α = b / sin β = c / sin γ
Maybe a sanity check could be added that the sum of the angles which have been entered is less than 180.
Maybe a function could be added to calculate the area of the triangle, according to the following formula:
A = sqrt( s (s-a) (s-b) (s-c) ) with s = ( a + b + c ) / 2
000 76 LBL
001 11 A
002 87 IFF
003 00 00
004 00 00
005 79 79
006 42 STO
007 01 01
008 92 RTN
009 76 LBL
010 12 B
011 87 IFF
012 00 00
013 00 00
014 82 82
015 42 STO
016 02 02
017 92 RTN
018 76 LBL
019 13 C
020 87 IFF
021 00 00
022 00 00
023 85 85
024 42 STO
025 03 03
026 92 RTN
027 76 LBL
028 16 A'
029 87 IFF
030 00 00
031 00 00
032 88 88
033 42 STO
034 04 04
035 92 RTN
036 76 LBL
037 17 B'
038 87 IFF
039 00 00
040 00 00
041 91 91
042 42 STO
043 05 05
044 92 RTN
045 76 LBL
046 18 C'
047 87 IFF
048 00 00
049 00 00
050 94 94
051 42 STO
052 06 06
053 92 RTN
054 76 LBL
055 14 D
056 22 INV
057 86 STF
058 00 00
059 22 INV
060 86 STF
061 01 01
062 05 5
063 69 OP
064 17 17
065 00 0
066 42 STO
067 01 01
068 42 STO
069 02 02
070 42 STO
071 03 03
072 42 STO
073 04 04
074 42 STO
075 05 05
076 42 STO
077 06 06
078 92 RTN
079 43 RCL
080 01 01
081 92 RTN
082 43 RCL
083 02 02
084 92 RTN
085 43 RCL
086 03 03
087 92 RTN
088 43 RCL
089 04 04
090 92 RTN
091 43 RCL
092 05 05
093 92 RTN
094 43 RCL
095 06 06
096 92 RTN
097 00 0
098 35 1/X
099 92 RTN
100 76 LBL
101 15 E
102 87 IFF
103 01 01
104 05 05
105 22 22
106 00 0
107 42 STO
108 09 09
109 42 STO
110 10 10
111 01 1
112 42 STO
113 07 07
114 01 1
115 01 1
116 42 STO
117 08 08
118 03 3
119 42 STO
120 00 00
121 29 CP
122 73 RC*
123 07 07
124 67 EQ
125 01 01
126 35 35
127 43 RCL
128 07 07
129 44 SUM
130 10 10
131 72 ST*
132 08 08
133 69 OP
134 28 28
135 69 OP
136 27 27
137 97 DSZ
138 00 00
139 01 01
140 22 22
141 03 3
142 42 STO
143 00 00
144 73 RC*
145 07 07
146 67 EQ
147 01 01
148 57 57
149 43 RCL
150 07 07
151 72 ST*
152 08 08
153 69 OP
154 29 29
155 69 OP
156 28 28
157 69 OP
158 27 27
159 97 DSZ
160 00 00
161 01 01
162 44 44
163 03 3
164 32 X#T
165 53 (
166 43 RCL
167 08 08
168 75 -
169 01 1
170 01 1
171 54 )
172 22 INV
173 67 EQ
174 00 00
175 97 97
176 43 RCL
177 09 09
178 32 X#T
179 67 EQ
180 00 00
181 97 97
182 09 9
183 48 EXC
184 10 10
185 22 INV
186 44 SUM
187 10 10
188 01 1
189 94 +/-
190 22 INV
191 39 COS
192 52 EE
193 22 INV
194 52 EE
195 42 STO
196 00 00
197 00 0
198 67 EQ
199 03 03
200 02 02
201 02 2
202 67 EQ
203 03 03
204 37 37
205 29 CP
206 73 RC*
207 10 10
208 67 EQ
209 04 04
210 27 27
211 43 RCL
212 11 11
213 42 STO
214 10 10
215 43 RCL
216 12 12
217 42 STO
218 08 08
219 43 RCL
220 13 13
221 42 STO
222 07 07
223 03 3
224 22 INV
225 44 SUM
226 13 13
227 44 SUM
228 10 10
229 44 SUM
230 08 08
231 53 (
232 73 RC*
233 11 11
234 33 X^2
235 85 +
236 73 RC*
237 12 12
238 33 X^2
239 75 -
240 02 2
241 65 *
242 73 RC*
243 11 11
244 65 *
245 73 RC*
246 12 12
247 65 *
248 73 RC*
249 07 07
250 39 COS
251 54 )
252 34 SQR
253 72 ST*
254 13 13
255 71 SBR
256 02 02
257 74 74
258 53 (
259 43 RCL
260 00 00
261 75 -
262 73 RC*
263 10 10
264 75 -
265 73 RC*
266 07 07
267 54 )
268 72 ST*
269 08 08
270 86 STF
271 00 00
272 00 0
273 92 RTN
274 53 (
275 53 (
276 73 RC*
277 12 12
278 33 X^2
279 85 +
280 73 RC*
281 13 13
282 33 X^2
283 75 -
284 73 RC*
285 11 11
286 33 X^2
287 54 )
288 55 /
289 02 2
290 55 /
291 73 RC*
292 12 12
293 55 /
294 73 RC*
295 13 13
296 54 )
297 22 INV
298 39 COS
299 72 ST*
300 10 10
301 92 RTN
302 04 4
303 42 STO
304 10 10
305 71 SBR
306 02 02
307 74 74
308 05 5
309 42 STO
310 10 10
311 43 RCL
312 11 11
313 48 EXC
314 13 13
315 48 EXC
316 12 12
317 42 STO
318 11 11
319 71 SBR
320 02 02
321 74 74
322 53 (
323 43 RCL
324 00 00
325 75 -
326 43 RCL
327 04 04
328 75 -
329 43 RCL
330 05 05
331 54 )
332 42 STO
333 06 06
334 61 GTO
335 02 02
336 70 70
337 53 (
338 01 1
339 05 5
340 75 -
341 43 RCL
342 12 12
343 75 -
344 43 RCL
345 13 13
346 54 )
347 42 STO
348 07 07
349 53 (
350 43 RCL
351 00 00
352 75 -
353 73 RC*
354 12 12
355 75 -
356 73 RC*
357 13 13
358 54 )
359 72 ST*
360 07 07
361 53 (
362 43 RCL
363 11 11
364 42 STO
365 12 12
366 85 +
367 01 1
368 75 -
369 53 (
370 40 INT
371 55 /
372 04 4
373 54 )
374 59 INT
375 65 *
376 02 2
377 54 )
378 42 STO
379 13 13
380 42 STO
381 07 07
382 03 3
383 44 SUM
384 12 12
385 44 SUM
386 07 07
387 71 SBR
388 04 04
389 12 12
390 53 (
391 06 6
392 75 -
393 43 RCL
394 11 11
395 75 -
396 43 RCL
397 13 13
398 54 )
399 42 STO
400 13 13
401 42 STO
402 07 07
403 03 3
404 44 SUM
405 07 07
406 71 SBR
407 04 04
408 12 12
409 61 GTO
410 02 02
411 70 70
412 53 (
413 73 RC*
414 07 07
415 38 SIN
416 55 /
417 73 RC*
418 12 12
419 38 SIN
420 65 *
421 73 RC*
422 11 11
423 54 )
424 72 ST*
425 13 13
426 92 RTN
427 43 RCL
428 13 13
429 42 STO
430 11 11
431 53 (
432 01 1
433 05 5
434 75 -
435 43 RCL
436 13 13
437 75 -
438 43 RCL
439 10 10
440 54 )
441 42 STO
442 12 12
443 42 STO
444 07 07
445 43 RCL
446 10 10
447 42 STO
448 08 08
449 03 3
450 22 INV
451 44 SUM
452 11 11
453 22 INV
454 44 SUM
455 12 12
456 22 INV
457 44 SUM
458 08 08
459 73 RC*
460 11 11
461 32 X#T
462 73 RC*
463 12 12
464 22 INV
465 77 GE
466 04 04
467 70 70
468 86 STF
469 01 01
470 53 (
471 73 RC*
472 12 12
473 55 /
474 73 RC*
475 11 11
476 65 *
477 73 RC*
478 13 13
479 38 SIN
480 54 )
481 22 INV
482 38 SIN
483 72 ST*
484 07 07
485 53 (
486 43 RCL
487 00 00
488 75 -
489 73 RC*
490 13 13
491 75 -
492 73 RC*
493 07 07
494 54 )
495 72 ST*
496 10 10
497 53 (
498 73 RC*
499 10 10
500 38 SIN
501 55 /
502 73 RC*
503 13 13
504 38 SIN
505 65 *
506 73 RC*
507 11 11
508 54 )
509 72 ST*
510 08 08
511 22 INV
512 87 IFF
513 01 01
514 02 02
515 70 70
516 86 STF
517 00 00
518 00 0
519 35 1/X
520 02 2
521 92 RTN
522 22 INV
523 86 STF
524 01 01
525 53 (
526 43 RCL
527 00 00
528 75 -
529 73 RC*
530 07 07
531 54 )
532 72 ST*
533 07 07
534 61 GTO
535 04 04
536 85 85