Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Tria
!Ignotum/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 » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Tria |
| Read OK: | ✔ |
| File size: | 04D8 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Triangles 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 73 69 6e 41 3d 6f 70 70 2f 68 79 70 |les.sinA=opp/hyp| 00000020 0a 54 68 69 73 20 69 73 20 74 68 65 20 64 65 66 |.This is the def| 00000030 69 6e 69 74 69 6f 6e 20 6f 66 20 74 68 65 20 74 |inition of the t| 00000040 68 65 20 73 69 6e 65 0a 6f 66 20 61 6e 20 61 6e |he sine.of an an| 00000050 67 6c 65 2e 20 0a 4e 6f 74 65 3a 20 49 74 20 6f |gle. .Note: It o| 00000060 6e 6c 79 20 61 70 70 6c 69 65 73 20 74 6f 20 72 |nly applies to r| 00000070 69 67 68 74 2d 61 6e 67 6c 65 64 0a 74 72 69 61 |ight-angled.tria| 00000080 6e 67 6c 65 73 0a 0a 63 6f 73 41 3d 61 64 6a 2f |ngles..cosA=adj/| 00000090 68 79 70 0a 54 68 69 73 20 69 73 20 74 68 65 20 |hyp.This is the | 000000a0 64 65 66 69 6e 69 74 69 6f 6e 20 6f 66 20 74 68 |definition of th| 000000b0 65 20 74 68 65 20 63 6f 73 69 6e 65 0a 6f 66 20 |e the cosine.of | 000000c0 61 6e 20 61 6e 67 6c 65 2e 20 0a 4e 6f 74 65 3a |an angle. .Note:| 000000d0 20 49 74 20 6f 6e 6c 79 20 61 70 70 6c 69 65 73 | It only applies| 000000e0 20 74 6f 20 72 69 67 68 74 2d 61 6e 67 6c 65 64 | to right-angled| 000000f0 0a 74 72 69 61 6e 67 6c 65 73 0a 0a 74 61 6e 41 |.triangles..tanA| 00000100 3d 6f 70 70 2f 61 64 6a 0a 54 68 69 73 20 69 73 |=opp/adj.This is| 00000110 20 74 68 65 20 64 65 66 69 6e 69 74 69 6f 6e 20 | the definition | 00000120 6f 66 20 74 68 65 20 74 68 65 20 74 61 6e 67 65 |of the the tange| 00000130 6e 74 0a 6f 66 20 61 6e 20 61 6e 67 6c 65 2e 20 |nt.of an angle. | 00000140 0a 4e 6f 74 65 3a 20 49 74 20 6f 6e 6c 79 20 61 |.Note: It only a| 00000150 70 70 6c 69 65 73 20 74 6f 20 72 69 67 68 74 2d |pplies to right-| 00000160 61 6e 67 6c 65 64 0a 74 72 69 61 6e 67 6c 65 73 |angled.triangles| 00000170 0a 0a 61 b2 3d 62 b2 2b 63 b2 0a 54 68 69 73 20 |..a.=b.+c..This | 00000180 69 73 20 70 79 74 68 61 67 6f 72 61 73 27 73 20 |is pythagoras's | 00000190 74 68 65 6f 72 65 6d 2c 20 77 68 65 72 65 20 61 |theorem, where a| 000001a0 2c 62 0a 61 6e 64 20 63 20 61 72 65 20 74 68 65 |,b.and c are the| 000001b0 20 73 69 64 65 20 6c 65 6e 67 74 68 73 20 6f 66 | side lengths of| 000001c0 20 74 68 65 0a 74 72 69 61 6e 67 6c 65 2c 20 61 | the.triangle, a| 000001d0 20 62 65 69 6e 67 20 74 68 65 20 68 79 70 6f 74 | being the hypot| 000001e0 65 6e 75 73 65 2e 0a 4e 6f 74 65 3a 20 49 74 20 |enuse..Note: It | 000001f0 6f 6e 6c 79 20 61 70 70 6c 69 65 73 20 74 6f 20 |only applies to | 00000200 72 69 67 68 74 2d 61 6e 67 6c 65 64 0a 74 72 69 |right-angled.tri| 00000210 61 6e 67 6c 65 73 0a 61 72 65 61 3d bd 61 62 73 |angles.area=.abs| 00000220 69 6e 43 0a 57 68 65 72 65 20 43 20 69 73 20 74 |inC.Where C is t| 00000230 68 65 20 61 6e 67 6c 65 20 62 65 74 77 65 65 6e |he angle between| 00000240 20 74 68 65 20 73 69 64 65 0a 6c 65 6e 67 74 68 | the side.length| 00000250 73 20 61 20 61 6e 64 20 62 2e 20 0a 4e 6f 74 65 |s a and b. .Note| 00000260 3a 20 49 74 20 61 70 70 6c 69 65 73 20 74 6f 20 |: It applies to | 00000270 61 6e 79 20 74 72 69 61 6e 67 6c 65 0a 0a 0a 61 |any triangle...a| 00000280 72 65 61 3d 28 73 28 73 2d 61 29 28 73 2d 62 29 |rea=(s(s-a)(s-b)| 00000290 28 73 2d 63 29 29 5e bd 0a 4b 6e 6f 77 6e 20 61 |(s-c))^..Known a| 000002a0 73 20 48 65 72 6f 27 73 20 66 6f 72 6d 75 6c 61 |s Hero's formula| 000002b0 2c 20 77 68 65 72 65 20 61 2c 20 62 20 61 6e 64 |, where a, b and| 000002c0 20 63 0a 61 72 65 20 73 69 64 65 20 6c 65 6e 67 | c.are side leng| 000002d0 74 68 73 20 61 6e 64 20 73 3d bd 28 61 2b 62 2b |ths and s=.(a+b+| 000002e0 63 29 2e 0a 4e 6f 74 65 3a 20 49 74 20 61 70 70 |c)..Note: It app| 000002f0 6c 69 65 73 20 74 6f 20 61 6e 79 20 74 72 69 61 |lies to any tria| 00000300 6e 67 6c 65 0a 0a 0a 61 2f 73 69 6e 41 3d 62 2f |ngle...a/sinA=b/| 00000310 73 69 6e 42 3d 63 2f 73 69 6e 43 0a 4b 6e 6f 77 |sinB=c/sinC.Know| 00000320 6e 20 61 73 20 74 68 65 20 73 69 6e 65 20 72 75 |n as the sine ru| 00000330 6c 65 2c 20 77 68 65 72 65 20 74 68 65 20 6c 6f |le, where the lo| 00000340 77 65 72 0a 63 61 73 65 20 6c 65 74 74 65 72 73 |wer.case letters| 00000350 20 61 72 65 20 74 68 65 20 73 69 64 65 20 6c 65 | are the side le| 00000360 6e 67 74 68 73 20 61 6e 64 20 74 68 65 0a 75 70 |ngths and the.up| 00000370 70 65 72 20 63 61 73 65 20 61 72 65 20 74 68 65 |per case are the| 00000380 20 61 6e 67 6c 65 73 20 6f 70 70 6f 73 69 74 65 | angles opposite| 00000390 20 74 68 65 73 65 0a 73 69 64 65 73 2e 0a 4e 6f | these.sides..No| 000003a0 74 65 3a 20 49 74 20 61 70 70 6c 69 65 73 20 74 |te: It applies t| 000003b0 6f 20 61 6e 79 20 74 72 69 61 6e 67 6c 65 0a 61 |o any triangle.a| 000003c0 b2 3d 62 b2 2b 63 b2 2d 32 62 63 63 6f 73 41 0a |.=b.+c.-2bccosA.| 000003d0 4b 6e 6f 77 6e 20 61 73 20 74 68 65 20 63 6f 73 |Known as the cos| 000003e0 69 6e 65 20 72 75 6c 65 2c 20 77 68 65 72 65 20 |ine rule, where | 000003f0 74 68 65 20 6c 6f 77 65 72 0a 63 61 73 65 20 6c |the lower.case l| 00000400 65 74 74 65 72 73 20 61 72 65 20 74 68 65 20 73 |etters are the s| 00000410 69 64 65 20 6c 65 6e 67 74 68 73 20 61 6e 64 0a |ide lengths and.| 00000420 61 6e 67 6c 65 20 41 20 69 73 20 74 68 65 20 61 |angle A is the a| 00000430 6e 67 6c 65 20 6f 70 70 6f 73 69 74 65 20 74 68 |ngle opposite th| 00000440 65 20 73 69 64 65 0a 6c 65 6e 67 74 68 20 61 2e |e side.length a.| 00000450 0a 4e 6f 74 65 3a 20 49 74 20 61 70 70 6c 69 65 |.Note: It applie| 00000460 73 20 74 6f 20 61 6e 79 20 74 72 69 61 6e 67 6c |s to any triangl| 00000470 65 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |e...............| 00000480 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 000004d0 0a 0a 0a 0a 0a 0a 0a 0a |........| 000004d8
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