Extended Law of Sines

GeoGebra Commands & Parameters

1. Sequence(((4 * cos(u)) + x(O), (4 * sin(u)) + y(O)), u, 0, (2 * π) - π / 180, π / 180) → l1, {(7.830234347090063, 0.6266491029516028), (7.829625127715628, 0.6964587287007369), (7.827797655166446, 0.7662470897616067), (7.824752486108359, 0.8359929279233782), (7.82049054812936, 0.905674997928104), (7.8150131394570455, 0.9752720739422355), (7.808321928563156, 1.0447629560222167), (7.800418953655351, 1.1141264765721925), (7.791306622056345, 1.1833415067918645), (7.780987709470614, 1.2523869631125262), (7.769465359138895, 1.321241813619324), (7.756743080880719, 1.3898850844577821), (7.742824750025286, 1.45829586622264), (7.727714606231004, 1.5264533203270627), (7.71141725219405, 1.5943366853502736), (7.693937652246337, 1.6619252833616858), (7.675281130843339, 1.7291985262195995), (7.655453370942205, 1.7961359218425499), (7.634460412270677, 1.8627170804513926), (7.61230864948733, 1.9289217207802298), (7.589004830233696, 1.994729676254278), (7.564556053078871, 2.0601209011328043), (7.538969765357212, 2.1250754766152515), (7.512253760899824, 2.1895736169086986), (7.484416177660467, 2.2535956752548043), (7.455465495236663, 2.3171221499144012), (7.425410532286731, 2.3801336901079133), (7.394260443843534, 2.442611101909791), (7.36202471852577, 2.504535354095167), (7.328713175647646, 2.5658875839369517), (7.294335962227818, 2.6266491029516037), (7.258903549898512, 2.6868014025918208), (7.222426731715767, 2.7463261598844237), (7.184916618871759, 2.8052052430117125), (7.146384637310229, 2.8634207168345913), (7.10684252424603, 2.9209548483557883), (7.066302324589852, 2.9777901121214967), (7.024776387279234, 3.033909195559797), (6.9822773615169496, 3.0892950042542373), (6.938818192917946, 3.143930667150954), (6.894412119565974, 3.1977995416977616), (6.84907266798115, 3.2508852189136337), (6.8028136489996385, 3.3031715283870375), (6.755649153566743, 3.3546425432015985), (6.707593548444667, 3.4052825847875936), (6.658661471836252, 3.455076227697795), (6.6088678289260505, 3.5040083043062094), (6.558227787340055, 3.5520639094282864), (6.506756772525494, 3.5992284048611816), (6.45447046305209, 3.6454874238426926), (6.4013847858362185, 3.690826875427517), (6.347515911289411, 3.735232948779488), (6.292880248392693, 3.7786921173784926), (6.237494439698254, 3.8211911431407763), (6.181375356259953, 3.8627170804513944), (6.124540092494245, 3.903257280107572), (6.067005960973048, 3.9427993931717715), (6.0087904871501685, 3.981331374733301), (5.949911404022879, 4.018841487577308), (5.890386646730277, 4.0553183057600535), (5.83023434709006, 4.090750718089359), (5.769472828075408, 4.125127931509188), (5.708120598233623, 4.158439474387313), (5.646196346048247, 4.190675199705076), (5.583718934246369, 4.221825288148272), (5.520707394052857, 4.251880251098204), (5.457180919393259, 4.280830933522008), (5.393158861047154, 4.308668516761366), (5.328660720753707, 4.335384521218755), (5.26370614527126, 4.360970808940412), (5.1983149203927335, 4.385419586095238), (5.132506964918685, 4.408723405348871), (5.066302324589849, 4.430875168132219), (4.999721165981005, 4.451868126803746), (4.932783770358055, 4.47169588670488), (4.865510527500141, 4.490352408107878), (4.797921929488729, 4.5078320080555905), (4.730038564465518, 4.524129362092545), (4.6618811103610955, 4.539239505886826), (4.593470328596236, 4.55315783674226), (4.524827057757779, 4.565880115000436), (4.455972207250981, 4.577402465332154), (4.386926750930319, 4.587721377917885), (4.317711720710647, 4.596833709516892), (4.248348200160671, 4.604736684424697), (4.17885731808069, 4.611427895318585), (4.109260242066558, 4.6169053039909), (4.039578172061832, 4.621167241969898), (3.9698323339000603, 4.624212411027986), (3.9000439728391907, 4.6260398835771674), (3.8302343470900633, 4.626649102951603), (3.760424721340922, 4.6260398835771674), (3.6906363602800525, 4.624212411027985), (3.6208905221182808, 4.621167241969898), (3.551208452113555, 4.616905303990899), (3.481611376099423, 4.6114278953185845), (3.412120494019442, 4.6047366844246955), (3.342756973469466, 4.59683370951689), (3.273541943249794, 4.587721377917883), (3.2044964869291324, 4.577402465332153), (3.135641636422334, 4.565880115000434), (3.0669983655838764, 4.5531578367422565), (2.998587583819018, 4.539239505886824), (2.9304301297145954, 4.524129362092542), (2.8625467646913845, 4.507832008055587), (2.7949581666799723, 4.490352408107874), (2.7276849238220584, 4.471695886704875), (2.660747528199108, 4.451868126803742), (2.5941663695902655, 4.430875168132214), (2.5279617292614285, 4.4087234053488675), (2.46215377378738, 4.385419586095233), (2.396762548908854, 4.360970808940406), (2.3318079734264066, 4.335384521218749), (2.26730983313296, 4.308668516761361), (2.203287774786854, 4.280830933522003), (2.139761300127258, 4.251880251098199), (2.0767497599337466, 4.221825288148267), (2.01427234813187, 4.190675199705071), (1.952348095946495, 4.158439474387308), (1.8909958661047106, 4.1251279315091836), (1.8302343470900593, 4.090750718089355), (1.7700820474498435, 4.05531830576005), (1.710557290157241, 4.018841487577305), (1.6516782070299532, 3.9813313747332977), (1.5934627332070748, 3.942799393171769), (1.5359286016858786, 3.9032572801075696), (1.4790933379201712, 3.8627170804513926), (1.422974254481871, 3.821191143140775), (1.3675884457874319, 3.7786921173784918), (1.3129527828907155, 3.735232948779488), (1.2590839083439085, 3.690826875427517), (1.2059982311280373, 3.6454874238426935), (1.1537119216546343, 3.5992284048611833), (1.1022409068400734, 3.5520639094282886), (1.0516008652540791, 3.504008304306212), (1.0018072223438783, 3.4550762276977984), (0.9528751457354643, 3.405282584787598), (0.9048195406133877, 3.3546425432016034), (0.857655045180493, 3.303171528387043), (0.8113960261989823, 3.25088521891364), (0.7660565746141583, 3.1977995416977687), (0.7216505012621877, 3.143930667150962), (0.6781913326631832, 3.089295004254246), (0.6356923069009004, 3.033909195559807), (0.5941663695902824, 2.9777901121215073), (0.553626169934105, 2.9209548483558), (0.5140840568699057, 2.8634207168346038), (0.4755520753083764, 2.8052052430117254), (0.4380419624643688, 2.7463261598844375), (0.4015651442816237, 2.6868014025918354), (0.3661327319523182, 2.6266491029516197), (0.3317555185324901, 2.5658875839369686), (0.29844397565436553, 2.5045353540951845), (0.2662082503366019, 2.4426111019098093), (0.23505816189340534, 2.3801336901079324), (0.2050031989434733, 2.3171221499144217), (0.17605251651966958, 2.2535956752548256), (0.14821493328031154, 2.1895736169087208), (0.12149892882292335, 2.125075476615275), (0.09591264110126563, 2.0601209011328283), (0.07146386394643889, 1.9947296762543034), (0.048160044692805215, 1.928921720780256), (0.02600828190945803, 1.86271708045142), (0.0050153232379299695, 1.796135921842578), (-0.014812436663203865, 1.7291985262196288), (-0.03346895806620198, 1.661925283361716), (-0.05094855801391507, 1.5943366853503047), (-0.06724591205087016, 1.5264533203270947), (-0.08235605584515238, 1.458295866222673), (-0.09627438670058597, 1.389885084457816), (-0.10899666495876303, 1.3212418136193589), (-0.12051901529048203, 1.2523869631125617), (-0.13083792787621285, 1.1833415067919009), (-0.13995025947522022, 1.11412647657223), (-0.1478532343830259, 1.0447629560222549), (-0.15454444527691535, 0.9752720739422744), (-0.16002185394923085, 0.9056749979281439), (-0.16428379192823028, 0.8359929279234188), (-0.167328960986318, 0.7662470897616482), (-0.16915643353550092, 0.6964587287007792), (-0.16976565290993673, 0.6266491029516028), (-0.16915643353550225, 0.5568394772025127), (-0.1673289609863211, 0.4870511161416436), (-0.16428379192823472, 0.41730527797987294), (-0.16002185394923707, 0.3476232079751478), (-0.1545444452769229, 0.278026131961017), (-0.14785323438303521, 0.20853524988103656), (-0.13995025947523088, 0.1391717293310612), (-0.13083792787622484, 0.06995669911139002), (-0.12051901529049536, 0.0009112427907289611), (-0.10899666495877769, -0.06794360771606833), (-0.0962743867006024, -0.13658687855452556), (-0.08235605584517014, -0.20499766031938305), (-0.0672459120508897, -0.27315511442380513), (-0.05094855801393594, -0.3410384794470155), (-0.033468958066224186, -0.4086270774584271), (-0.014812436663227402, -0.47590032031634033), (0.005015323237904656, -0.5428377159392901), (0.026008281909431386, -0.6094188745481324), (0.04816004469277724, -0.6756235148769689), (0.07146386394640958, -0.7414314703510168), (0.09591264110123499, -0.8068226952295425), (0.12149892882289093, -0.8717772707119893), (0.1482149332802778, -0.9362754110054357), (0.1760525165196345, -1.0002974693515412), (0.20500319894343688, -1.063823944011138), (0.23505816189336715, -1.1268354842046495), (0.26620825033656237, -1.189312896006527), (0.2984439756543247, -1.2512371481919027), (0.3317555185324479, -1.3125893780336875), (0.36613273195227514, -1.3733508970483392), (0.4015651442815793, -1.433503196688556), (0.43804196246432303, -1.493027953981159), (0.4755520753083293, -1.5519070371084474), (0.5140840568698573, -1.6101225109313266), (0.5536261699340557, -1.6676566424525237), (0.5941663695902317, -1.7244919062182316), (0.6356923069008484, -1.7806109896565325), (0.6781913326631304, -1.8359967983509726), (0.721650501262133, -1.8906324612476895), (0.7660565746141033, -1.9445013357944974), (0.8113960261989259, -1.9975870130103694), (0.8576550451804352, -2.0498733224837733), (0.9048195406133286, -2.1013443372983347), (0.9528751457354048, -2.1519843788843303), (1.0018072223438175, -2.2017780217945315), (1.051600865254017, -2.2507100984029464), (1.1022409068400103, -2.2987657035250244), (1.15371192165457, -2.34593019895792), (1.2059982311279724, -2.3921892179394315), (1.2590839083438428, -2.4375286695242564), (1.3129527828906484, -2.4819347428762284), (1.367588445787364, -2.5253939114752333), (1.4229742544818023, -2.5678929372375174), (1.4790933379201014, -2.6094188745481364), (1.535928601685808, -2.6499590742043146), (1.5934627332070033, -2.689501187268515), (1.6516782070298808, -2.7280331688300454), (1.7105572901571677, -2.765543281674054), (1.7700820474497694, -2.8020200998568), (1.8302343470899847, -2.8374525121861063), (1.890995866104635, -2.871829725605936), (1.9523480959464188, -2.9051412684840616), (2.0142723481317932, -2.9373769938018266), (2.0767497599336693, -2.968527082245024), (2.13976130012718, -2.998582045194957), (2.203287774786775, -3.027532727618762), (2.2673098331328796, -3.055370310858121), (2.3318079734263253, -3.0820863153155105), (2.3967625489087707, -3.107672603037169), (2.4621537737872954, -3.132121380191997), (2.5279617292613423, -3.155425199445632), (2.5941663695901784, -3.1775769622289807), (2.66074752819902, -3.1985699209005096), (2.7276849238219687, -3.2183976808016443), (2.7949581666798813, -3.237054202204644), (2.862546764691292, -3.254533802152358), (2.9304301297145017, -3.2708311561893146), (2.9985875838189235, -3.2859412999835977), (3.06699836558378, -3.2998596308390327), (3.1356416364222373, -3.312581909097211), (3.2044964869290338, -3.3241042594289314), (3.2735419432496946, -3.3344231720146635), (3.342756973469365, -3.3435355036136722), (3.4121204940193404, -3.3514384785214792), (3.4816113760993206, -3.3581296894153696), (3.551208452113451, -3.3636070980876864), (3.620890522118176, -3.3678690360666867), (3.690636360279947, -3.3709142051247762), (3.7604247213408155, -3.37274167767396), (3.8302343470900633, -3.373350897048397), (3.9000439728390823, -3.372741677673964), (3.969832333899951, -3.3709142051247842), (4.039578172061722, -3.3678690360666987), (4.109260242066447, -3.3636070980877024), (4.178857318080578, -3.3581296894153896), (4.248348200160558, -3.351438478521503), (4.317711720710534, -3.3435355036136998), (4.386926750930206, -3.334423172014695), (4.455972207250866, -3.324104259428967), (4.524827057757664, -3.3125819090972506), (4.593470328596122, -3.2998596308390766), (4.661881110360979, -3.2859412999836457), (4.730038564465402, -3.270831156189366), (4.797921929488613, -3.2545338021524133), (4.8655105275000246, -3.237054202204703), (4.932783770357938, -3.218397680801708), (4.999721165980888, -3.1985699209005767), (5.0663023245897305, -3.1775769622290513), (5.1325069649185675, -3.1554251994457068), (5.198314920392615, -3.1321213801920753), (5.263706145271142, -3.1076726030372512), (5.328660720753589, -3.082086315315596), (5.393158861047036, -3.05537031085821), (5.457180919393142, -3.0275327276188553), (5.52070739405274, -2.998582045195054), (5.583718934246251, -2.9685270822451244), (5.6461963460481295, -2.9373769938019305), (5.7081205982335055, -2.905141268484169), (5.769472828075291, -2.871829725606047), (5.830234347089943, -2.837452512186221), (5.89038664673016, -2.802020099856918), (5.949911404022765, -2.765543281674175), (6.008790487150054, -2.7280331688301698), (6.067005960972933, -2.689501187268643), (6.124540092494131, -2.6499590742044457), (6.18137535625984, 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(7.808321928563138, 0.20853524988080896), (7.8150131394570295, 0.27802613196078907), (7.820490548129348, 0.3476232079749195), (7.824752486108349, 0.4173052779796444), (7.82779765516644, 0.4870511161414149), (7.829625127715625, 0.5568394772022839)}
2. Circle(O, 4) → c
3. Point(l1) → C
4. Point(l1) → A
5. Point(l1) → B
6. Polygon(B, C, A) → t1, d, b, c_1
7. InteriorAngles(t1) → α, β, γ
8. Point(xAxis) → D
9. OrthogonalLine(D, xAxis) → f
10. Point(f) → E
11. Point(f) → F
12. Point(f) → G