Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars » StarInfo/Allen/!Ignotum/Formulae/Formulae/Tria
StarInfo/Allen/!Ignotum/Formulae/Formulae/Tria
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars |
| Filename: | StarInfo/Allen/!Ignotum/Formulae/Formulae/Tria |
| Read OK: | ✔ |
| File size: | 065C bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Triangles # New entries should take the form of: # Formula # Note 1 # Note 2 # Note 3 # Note 4 # Note 5 # Formula # Note 1 # And so on... # To fit snugly into the window, each line should be no longer # than 42 characters. # There is a limit of 25 formulas per topic. # Any notes should be made here, at the beginning and should # be preceeded by a hash (#). sinA=opp/hyp This is the definition of the the sine of an angle. Note: It only applies to right-angled triangles cosA=adj/hyp This is the definition of the the cosine of an angle. Note: It only applies to right-angled triangles tanA=opp/adj This is the definition of the the tangent of an angle. Note: It only applies to right-angled triangles a�=b�+c� This is pythagoras's theorem, where a,b and c are the side lengths of the triangle, a being the hypotenuse. Note: It only applies to right-angled triangles area=�absinC Where C is the angle between the side lengths a and b. Note: It applies to any triangle area=(s(s-a)(s-b)(s-c))^� Known as Hero's formula, where a, b and c are side lengths and s=�(a+b+c). Note: It applies to any triangle a/sinA=b/sinB=c/sinC Known as the sine rule, where the lower case letters are the side lengths and the upper case are the angles opposite these sides. Note: It applies to any triangle a�=b�+c�-2bccosA Known as the cosine rule, where the lower case letters are the side lengths and angle A is the angle opposite the side length a. Note: It applies to any triangle
00000000 23 20 4d 61 74 68 73 20 3e 20 54 72 69 61 6e 67 |# Maths > Triang| 00000010 6c 65 73 0a 0a 23 20 4e 65 77 20 65 6e 74 72 69 |les..# New entri| 00000020 65 73 20 73 68 6f 75 6c 64 20 74 61 6b 65 20 74 |es should take t| 00000030 68 65 20 66 6f 72 6d 20 6f 66 3a 0a 23 20 20 20 |he form of:.# | 00000040 20 20 46 6f 72 6d 75 6c 61 0a 23 20 20 20 20 20 | Formula.# | 00000050 4e 6f 74 65 20 31 0a 23 20 20 20 20 20 4e 6f 74 |Note 1.# Not| 00000060 65 20 32 0a 23 20 20 20 20 20 4e 6f 74 65 20 33 |e 2.# Note 3| 00000070 0a 23 20 20 20 20 20 4e 6f 74 65 20 34 0a 23 20 |.# Note 4.# | 00000080 20 20 20 20 4e 6f 74 65 20 35 0a 23 20 20 20 20 | Note 5.# | 00000090 20 46 6f 72 6d 75 6c 61 0a 23 20 20 20 20 20 4e | Formula.# N| 000000a0 6f 74 65 20 31 0a 23 20 20 20 20 20 41 6e 64 20 |ote 1.# And | 000000b0 73 6f 20 6f 6e 2e 2e 2e 0a 23 20 54 6f 20 66 69 |so on....# To fi| 000000c0 74 20 73 6e 75 67 6c 79 20 69 6e 74 6f 20 74 68 |t snugly into th| 000000d0 65 20 77 69 6e 64 6f 77 2c 20 65 61 63 68 20 6c |e window, each l| 000000e0 69 6e 65 20 73 68 6f 75 6c 64 20 62 65 20 6e 6f |ine should be no| 000000f0 20 6c 6f 6e 67 65 72 0a 23 20 74 68 61 6e 20 34 | longer.# than 4| 00000100 32 20 63 68 61 72 61 63 74 65 72 73 2e 0a 23 20 |2 characters..# | 00000110 54 68 65 72 65 20 69 73 20 61 20 6c 69 6d 69 74 |There is a limit| 00000120 20 6f 66 20 32 35 20 66 6f 72 6d 75 6c 61 73 20 | of 25 formulas | 00000130 70 65 72 20 74 6f 70 69 63 2e 0a 0a 23 20 41 6e |per topic...# An| 00000140 79 20 6e 6f 74 65 73 20 73 68 6f 75 6c 64 20 62 |y notes should b| 00000150 65 20 6d 61 64 65 20 68 65 72 65 2c 20 61 74 20 |e made here, at | 00000160 74 68 65 20 62 65 67 69 6e 6e 69 6e 67 20 61 6e |the beginning an| 00000170 64 20 73 68 6f 75 6c 64 0a 23 20 62 65 20 70 72 |d should.# be pr| 00000180 65 63 65 65 64 65 64 20 62 79 20 61 20 68 61 73 |eceeded by a has| 00000190 68 20 28 23 29 2e 0a 0a 73 69 6e 41 3d 6f 70 70 |h (#)...sinA=opp| 000001a0 2f 68 79 70 0a 54 68 69 73 20 69 73 20 74 68 65 |/hyp.This is the| 000001b0 20 64 65 66 69 6e 69 74 69 6f 6e 20 6f 66 20 74 | definition of t| 000001c0 68 65 20 74 68 65 20 73 69 6e 65 0a 6f 66 20 61 |he the sine.of a| 000001d0 6e 20 61 6e 67 6c 65 2e 20 0a 4e 6f 74 65 3a 20 |n angle. .Note: | 000001e0 49 74 20 6f 6e 6c 79 20 61 70 70 6c 69 65 73 20 |It only applies | 000001f0 74 6f 20 72 69 67 68 74 2d 61 6e 67 6c 65 64 0a |to right-angled.| 00000200 74 72 69 61 6e 67 6c 65 73 0a 0a 63 6f 73 41 3d |triangles..cosA=| 00000210 61 64 6a 2f 68 79 70 0a 54 68 69 73 20 69 73 20 |adj/hyp.This is | 00000220 74 68 65 20 64 65 66 69 6e 69 74 69 6f 6e 20 6f |the definition o| 00000230 66 20 74 68 65 20 74 68 65 20 63 6f 73 69 6e 65 |f the the cosine| 00000240 0a 6f 66 20 61 6e 20 61 6e 67 6c 65 2e 20 0a 4e |.of an angle. .N| 00000250 6f 74 65 3a 20 49 74 20 6f 6e 6c 79 20 61 70 70 |ote: It only app| 00000260 6c 69 65 73 20 74 6f 20 72 69 67 68 74 2d 61 6e |lies to right-an| 00000270 67 6c 65 64 0a 74 72 69 61 6e 67 6c 65 73 0a 0a |gled.triangles..| 00000280 74 61 6e 41 3d 6f 70 70 2f 61 64 6a 0a 54 68 69 |tanA=opp/adj.Thi| 00000290 73 20 69 73 20 74 68 65 20 64 65 66 69 6e 69 74 |s is the definit| 000002a0 69 6f 6e 20 6f 66 20 74 68 65 20 74 68 65 20 74 |ion of the the t| 000002b0 61 6e 67 65 6e 74 0a 6f 66 20 61 6e 20 61 6e 67 |angent.of an ang| 000002c0 6c 65 2e 20 0a 4e 6f 74 65 3a 20 49 74 20 6f 6e |le. .Note: It on| 000002d0 6c 79 20 61 70 70 6c 69 65 73 20 74 6f 20 72 69 |ly applies to ri| 000002e0 67 68 74 2d 61 6e 67 6c 65 64 0a 74 72 69 61 6e |ght-angled.trian| 000002f0 67 6c 65 73 0a 0a 61 b2 3d 62 b2 2b 63 b2 0a 54 |gles..a.=b.+c..T| 00000300 68 69 73 20 69 73 20 70 79 74 68 61 67 6f 72 61 |his is pythagora| 00000310 73 27 73 20 74 68 65 6f 72 65 6d 2c 20 77 68 65 |s's theorem, whe| 00000320 72 65 20 61 2c 62 0a 61 6e 64 20 63 20 61 72 65 |re a,b.and c are| 00000330 20 74 68 65 20 73 69 64 65 20 6c 65 6e 67 74 68 | the side length| 00000340 73 20 6f 66 20 74 68 65 0a 74 72 69 61 6e 67 6c |s of the.triangl| 00000350 65 2c 20 61 20 62 65 69 6e 67 20 74 68 65 20 68 |e, a being the h| 00000360 79 70 6f 74 65 6e 75 73 65 2e 0a 4e 6f 74 65 3a |ypotenuse..Note:| 00000370 20 49 74 20 6f 6e 6c 79 20 61 70 70 6c 69 65 73 | It only applies| 00000380 20 74 6f 20 72 69 67 68 74 2d 61 6e 67 6c 65 64 | to right-angled| 00000390 0a 74 72 69 61 6e 67 6c 65 73 0a 61 72 65 61 3d |.triangles.area=| 000003a0 bd 61 62 73 69 6e 43 0a 57 68 65 72 65 20 43 20 |.absinC.Where C | 000003b0 69 73 20 74 68 65 20 61 6e 67 6c 65 20 62 65 74 |is the angle bet| 000003c0 77 65 65 6e 20 74 68 65 20 73 69 64 65 0a 6c 65 |ween the side.le| 000003d0 6e 67 74 68 73 20 61 20 61 6e 64 20 62 2e 20 0a |ngths a and b. .| 000003e0 4e 6f 74 65 3a 20 49 74 20 61 70 70 6c 69 65 73 |Note: It applies| 000003f0 20 74 6f 20 61 6e 79 20 74 72 69 61 6e 67 6c 65 | to any triangle| 00000400 0a 0a 0a 61 72 65 61 3d 28 73 28 73 2d 61 29 28 |...area=(s(s-a)(| 00000410 73 2d 62 29 28 73 2d 63 29 29 5e bd 0a 4b 6e 6f |s-b)(s-c))^..Kno| 00000420 77 6e 20 61 73 20 48 65 72 6f 27 73 20 66 6f 72 |wn as Hero's for| 00000430 6d 75 6c 61 2c 20 77 68 65 72 65 20 61 2c 20 62 |mula, where a, b| 00000440 20 61 6e 64 20 63 0a 61 72 65 20 73 69 64 65 20 | and c.are side | 00000450 6c 65 6e 67 74 68 73 20 61 6e 64 20 73 3d bd 28 |lengths and s=.(| 00000460 61 2b 62 2b 63 29 2e 0a 4e 6f 74 65 3a 20 49 74 |a+b+c)..Note: It| 00000470 20 61 70 70 6c 69 65 73 20 74 6f 20 61 6e 79 20 | applies to any | 00000480 74 72 69 61 6e 67 6c 65 0a 0a 0a 61 2f 73 69 6e |triangle...a/sin| 00000490 41 3d 62 2f 73 69 6e 42 3d 63 2f 73 69 6e 43 0a |A=b/sinB=c/sinC.| 000004a0 4b 6e 6f 77 6e 20 61 73 20 74 68 65 20 73 69 6e |Known as the sin| 000004b0 65 20 72 75 6c 65 2c 20 77 68 65 72 65 20 74 68 |e rule, where th| 000004c0 65 20 6c 6f 77 65 72 0a 63 61 73 65 20 6c 65 74 |e lower.case let| 000004d0 74 65 72 73 20 61 72 65 20 74 68 65 20 73 69 64 |ters are the sid| 000004e0 65 20 6c 65 6e 67 74 68 73 20 61 6e 64 20 74 68 |e lengths and th| 000004f0 65 0a 75 70 70 65 72 20 63 61 73 65 20 61 72 65 |e.upper case are| 00000500 20 74 68 65 20 61 6e 67 6c 65 73 20 6f 70 70 6f | the angles oppo| 00000510 73 69 74 65 20 74 68 65 73 65 0a 73 69 64 65 73 |site these.sides| 00000520 2e 0a 4e 6f 74 65 3a 20 49 74 20 61 70 70 6c 69 |..Note: It appli| 00000530 65 73 20 74 6f 20 61 6e 79 20 74 72 69 61 6e 67 |es to any triang| 00000540 6c 65 0a 61 b2 3d 62 b2 2b 63 b2 2d 32 62 63 63 |le.a.=b.+c.-2bcc| 00000550 6f 73 41 0a 4b 6e 6f 77 6e 20 61 73 20 74 68 65 |osA.Known as the| 00000560 20 63 6f 73 69 6e 65 20 72 75 6c 65 2c 20 77 68 | cosine rule, wh| 00000570 65 72 65 20 74 68 65 20 6c 6f 77 65 72 0a 63 61 |ere the lower.ca| 00000580 73 65 20 6c 65 74 74 65 72 73 20 61 72 65 20 74 |se letters are t| 00000590 68 65 20 73 69 64 65 20 6c 65 6e 67 74 68 73 20 |he side lengths | 000005a0 61 6e 64 0a 61 6e 67 6c 65 20 41 20 69 73 20 74 |and.angle A is t| 000005b0 68 65 20 61 6e 67 6c 65 20 6f 70 70 6f 73 69 74 |he angle opposit| 000005c0 65 20 74 68 65 20 73 69 64 65 0a 6c 65 6e 67 74 |e the side.lengt| 000005d0 68 20 61 2e 0a 4e 6f 74 65 3a 20 49 74 20 61 70 |h a..Note: It ap| 000005e0 70 6c 69 65 73 20 74 6f 20 61 6e 79 20 74 72 69 |plies to any tri| 000005f0 61 6e 67 6c 65 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |angle...........| 00000600 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 00000650 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |............| 0000065c
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