File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/3G30-aX6FuGMr.js.map
{"version":3,"file":"3G30-aX6FuGMr.js","sources":["../../src/exercices/3e/3G30.js"],"sourcesContent":["import Decimal from 'decimal.js'\nimport { codageAngle, codageAngleDroit } from '../../lib/2d/angles.js'\nimport { milieu, point } from '../../lib/2d/points.js'\nimport { barycentre, nommePolygone, polygone } from '../../lib/2d/polygones.js'\nimport { longueur, segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { latexParPoint } from '../../lib/2d/textes.js'\nimport { homothetie, rotation } from '../../lib/2d/transformations.js'\nimport { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { texteEnCouleurEtGras } from '../../lib/outils/embellissements'\nimport { quatriemeProportionnelle } from '../../lib/outils/calculs'\nimport { deprecatedTexFraction } from '../../lib/outils/deprecatedFractions.js'\nimport { creerNomDePolygone, numAlpha } from '../../lib/outils/outilString.js'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { context } from '../../modules/context.js'\nimport Grandeur from '../../modules/Grandeur'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport Exercice from '../Exercice.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\n\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const amcReady = true\nexport const amcType = 'AMCHybride'\nexport const dateDeModifImportante = '21/03/2022'\n\nexport const titre = 'Calculate a length in a right triangle using trigonometry'\n\n/**\n * @author Jean-Claude Lhote à partir de 3G30-1 de Rémi Angot\n * 3G30 Exercice remplaçant l'exercice initial utilisant MG32\n * Calculer une longueur en utilisant l'un des trois rapport trigonométrique.\n * * Si this.level=4 alors seul le cosinus sera utilisé.\n * Mars 2021\n * combinaisonListes des questions par Guillaume Valmont le 23/05/2022\n */\nexport const uuid = 'bd6b1'\nexport const ref = '3G30'\nexport default function CalculDeLongueur () {\n Exercice.call(this)\n this.nbQuestions = 3\n this.nbCols = 1\n this.nbColsCorr = 1\n this.sup = false\n this.correctionDetailleeDisponible = true\n this.correctionDetaillee = false\n this.interactif = false\n if (context.isHtml) {\n this.spacing = 2\n this.spacingCorr = 3\n } else {\n this.spacing = 2\n this.spacingCorr = 2\n }\n\n this.nouvelleVersion = function () {\n this.consigne = ''\n this.autoCorrection = []\n this.listeQuestions = []\n this.listeCorrections = []\n let reponse\n let listeDeNomsDePolygones\n let typeQuestionsDisponibles = ['cosine', 'sinus', 'tangent', 'invCosine', 'invSinus', 'invTangent']\n if (this.level === 4) typeQuestionsDisponibles = ['cosine', 'invCosine']\n\n const listeTypeQuestions = combinaisonListes(typeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0; i < this.nbQuestions; i++) {\n const unite = choice(['m', 'cm', 'dm', 'mm'])\n if (i % 3 === 0) listeDeNomsDePolygones = ['Q.D.']\n const nom = creerNomDePolygone(3, listeDeNomsDePolygones)\n listeDeNomsDePolygones.push(nom)\n let texte = ''\n let texteAMC = ''\n let q2AMC = ''\n let nom1, nom2\n let texteCorr = ''\n const objetsEnonce = []\n const objetsCorrection = []\n let ab, bc, ac\n\n const angleABC = randint(35, 55)\n const angleABCr = Decimal.acos(-1).div(180).mul(angleABC)\n if (!context.isHtml && this.sup) {\n // text += '\\\\begin{minipage}{.7\\\\linewidth}\\n'\n }\n switch (listeTypeQuestions[i]) {\n case 'cosine': // AB=BCxcos(B)\n bc = new Decimal(randint(10, 15))\n ab = Decimal.cos(angleABCr).mul(bc)\n ac = Decimal.sin(angleABCr).mul(bc)\n texteAMC += `In the right triangle $${nom}$ in $${nom[0]}$,<br> $${nom[1] + nom[2]} = ${bc}$ ${unite} and $\\\\widehat{${nom}} = ${angleABC}\\\\degree$.<br>`\n nom1 = nom[0]\n nom2 = nom[1]\n break\n case 'sinus':\n bc = new Decimal(randint(10, 15))\n ab = Decimal.cos(angleABCr).mul(bc)\n ac = Decimal.sin(angleABCr).mul(bc)\n texteAMC += `In the right triangle $${nom}$ in $${nom[0]}$,<br> $${nom[1] + nom[2]} = ${bc}$ ${unite} and $\\\\widehat{${nom}} = ${angleABC}\\\\degree$.<br>`\n nom1 = nom[0]\n nom2 = nom[2]\n break\n case 'tangent':\n ab = new Decimal(randint(7, 10))\n ac = Decimal.tan(angleABCr).mul(ab)\n bc = new Decimal(ab).div(Decimal.cos(angleABCr))\n texteAMC += `In the right triangle $${nom}$ in $${nom[0]}$,<br> $${nom[0] + nom[1]} = ${ab}$ ${unite} and $\\\\widehat{${nom}} = ${angleABC}\\\\degree$.<br>`\n nom1 = nom[0]\n nom2 = nom[2]\n break\n case 'invCosine':\n ab = new Decimal(randint(7, 10))\n bc = new Decimal(ab).div(Decimal.cos(angleABCr))\n ac = Decimal.sin(angleABCr).mul(bc)\n texteAMC += `In the right triangle $${nom}$ in $${nom[0]}$,<br> $${nom[0] + nom[1]} = ${ab}$ ${unite} and $\\\\widehat{${nom}} = ${angleABC}\\\\degree$.<br>`\n nom1 = nom[1]\n nom2 = nom[2]\n break\n case 'invSinus':\n ac = new Decimal(randint(7, 10))\n bc = new Decimal(ac).div(Decimal.sin(angleABCr))\n ab = Decimal.cos(angleABCr).mul(bc)\n texteAMC += `In the right triangle $${nom}$ in $${nom[0]}$,<br> $${nom[0] + nom[2]} = ${ac}$ ${unite} and $\\\\widehat{${nom}} = ${angleABC}\\\\degree$.<br>`\n nom1 = nom[1]\n nom2 = nom[2]\n break\n case 'invTangent':\n ac = new Decimal(randint(7, 10))\n bc = new Decimal(ac).div(Decimal.sin(angleABCr))\n ab = Decimal.cos(angleABCr).mul(bc)\n texteAMC += `In the right triangle $${nom}$ in $${nom[0]}$,<br> $${nom[0] + nom[2]} = ${ac}$ ${unite} and $\\\\widehat{${nom}} = ${angleABC}\\\\degree$.<br>`\n nom1 = nom[0]\n nom2 = nom[1]\n break\n }\n texte += texteAMC + `Calculate $${nom1 + nom2}$ to the nearest $0.1$ ${unite}.`\n q2AMC = `Calculate $${nom1 + nom2}$ to the tenth of ${unite}.`\n\n if (!context.isHtml && this.sup) {\n // text += '\\n\\\\end{minipage}\\n'\n }\n const a = point(0, 0)\n const b = point(ab, 0)\n const c = point(0, ac)\n const p1 = polygone(a, b, c)\n // p1.isVisible = false\n const p2 = rotation(p1, a, randint(0, 360))\n const A = p2.listePoints[0]\n const B = p2.listePoints[1]\n const C = p2.listePoints[2]\n const codage = codageAngleDroit(B, A, C)\n A.nom = nom[0]\n B.nom = nom[1]\n C.nom = nom[2]\n const nomme = nommePolygone(p2, nom)\n const hypo = segment(C, B, 'blue')\n hypo.epaisseur = 2\n const codageDeAngle = codageAngle(A, B, C, 2)\n const mAB = milieu(A, B)\n const mAC = milieu(A, C)\n const mBC = milieu(B, C)\n const G = barycentre(p2)\n const m3 = homothetie(mBC, G, 1 + 1.5 / longueur(G, mBC), 'm3', 'center')\n const m1 = homothetie(mAB, mBC, 1 + 1.5 / longueur(mBC, mAB), 'm1', 'center')\n const m2 = homothetie(mAC, mBC, 1 + 1.5 / longueur(mBC, mAC), 'm2', 'center')\n let m4\n let t1, t2, t3\n let nomLongueur // la longueur à déterminer\n let calcul0, calcul1, calcul2, calcul3, calcul4, calcul5 // les propsitions de calcul pour AMC\n let calculTrue\n switch (listeTypeQuestions[i]) {\n case 'cosine': // AB=BCxcos(B)\n t3 = latexParPoint(`${bc} \\\\text{ ${unite}}`, m3, 'black', 120, 12, '')\n t2 = latexParPoint('?', m1, 'black', 120, 12, '')\n m4 = homothetie(G, B, 2.7 / longueur(B, G), 'B2', 'center')\n t1 = latexParPoint(`${angleABC}\\\\degree`, m4, 'black', 20, 12, '')\n break\n case 'sinus':\n t3 = latexParPoint(`${bc} \\\\text{ ${unite}}`, m3, 'black', 120, 12, '')\n t2 = latexParPoint('?', m2, 'black', 120, 12, '')\n m4 = homothetie(G, B, 2.7 / longueur(B, G), 'B2', 'center')\n t1 = latexParPoint(`${angleABC}\\\\degree`, m4, 'black', 100, 12, '')\n break\n case 'tangent':\n t1 = latexParPoint(`${ab} \\\\text{ ${unite}}`, m1, 'black', 120, 12, '')\n t2 = latexParPoint('?', m2, 'black', 120, 12, '')\n m4 = homothetie(G, B, 2.7 / longueur(B, G), 'B2', 'center')\n t3 = latexParPoint(`${angleABC}\\\\degree`, m4, 'black', 100, 12, '')\n break\n case 'invCosine':\n t1 = latexParPoint(`${ab} \\\\text{ ${unite}}`, m1, 'black', 120, 12, '')\n t3 = latexParPoint('?', m3, 'black', 120, 12, '')\n m4 = homothetie(G, B, 2.7 / longueur(B, G), 'B2', 'center')\n t2 = latexParPoint(`${angleABC}\\\\degree`, m4, 'black', 100, 12, '')\n break\n case 'invSinus':\n t2 = latexParPoint(`${ac} \\\\text{ ${unite}}`, m2, 'black', 120, 12, '')\n t3 = latexParPoint('?', m3, 'black', 120, 12, '')\n m4 = homothetie(G, B, 2.7 / longueur(B, G), 'B2', 'center')\n t1 = latexParPoint(`${angleABC}\\\\degree`, m4, 'black', 100, 12, '')\n break\n case 'invTangent':\n t2 = latexParPoint(`${ac} \\\\text{ ${unite}}`, m2, 'black', 120, 12, '')\n t1 = latexParPoint('?', m1, 'black', 120, 12, '')\n m4 = homothetie(G, B, 2.7 / longueur(B, G), 'B2', 'center')\n t3 = latexParPoint(`${angleABC}\\\\degree`, m4, 'black', 100, 12, '')\n break\n }\n objetsEnonce.push(p2, codage, nomme, t1, t2, t3, codageDeAngle)\n objetsCorrection.push(p2, codage, nomme, t1, t2, t3, hypo, codageDeAngle)\n\n const paramsEnonce = {\n xmin: Math.min(A.x, B.x, C.x) - 2,\n ymin: Math.min(A.y, B.y, C.y) - 2,\n xmax: Math.max(A.x, B.x, C.x) + 2,\n ymax: Math.max(A.y, B.y, C.y) + 2,\n pixelsParCm: 20,\n scale: 0.37,\n mainlevee: true,\n amplitude: context.isHtml ? 0.4 : 1\n }\n const paramsCorrection = {\n xmin: Math.min(A.x, B.x, C.x) - 4,\n ymin: Math.min(A.y, B.y, C.y) - 4,\n xmax: Math.max(A.x, B.x, C.x) + 2,\n ymax: Math.max(A.y, B.y, C.y) + 2,\n pixelsParCm: 20,\n scale: 0.35,\n mainlevee: false\n }\n if (!context.isHtml && this.sup) {\n texte += '\\\\\\\\' // \\\\begin{minipage}{.3\\\\linewidth}\\n'\n }\n if (this.sup) {\n texte += mathalea2d(paramsEnonce, objetsEnonce) + '<br>'\n }\n if (!context.isHtml && this.correctionDetaillee) {\n texteCorr += '\\\\begin{minipage}{.4\\\\linewidth}\\n' + mathalea2d(paramsCorrection, objetsCorrection) + '\\n\\\\end{minipage}\\n' + '\\\\begin{minipage}{.7\\\\linewidth}\\n'\n }\n if (!context.isHtml && this.sup) {\n // text += '\\n\\\\end{minipage}\\n'\n }\n switch (listeTypeQuestions[i]) {\n case 'cosine': // AB=BCxcos(B)\n texteCorr += `In the right triangle $${nom}$ in $${nom[0]}$,<br> the cosine of the angle $\\\\widehat{${nom}}$ is defined by:<br>`\n texteCorr += `$\\\\cos\\\\left(\\\\widehat{${nom}}\\\\right)=\\\\dfrac{${nom[0] + nom[1]}}{${nom[1] + nom[2]}}$.<br>`\n texteCorr += 'With digital data:<br>'\n texteCorr += `$\\\\dfrac{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}{\\\\color{red}{1}} = ${deprecatedTexFraction(nom[0] + nom[1], bc)}$<br>`\n texteCorr += `${texteEnCouleurEtGras('The cross products are equal, therefore: ', 'red')}<br>`\n texteCorr += `$${nom[0] + nom[1]} = ${quatriemeProportionnelle('\\\\color{red}{1}', bc, `\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)`)}$`\n texteCorr += `i.e. $${nom[0] + nom[1]}\\\\approx${texNombre(ab, 1)}$ ${unite}.`\n reponse = ab.toDP(1)\n nomLongueur = `$${nom[0] + nom[1]}$`\n calcul0 = `$${nom[1] + nom[2]}\\\\times\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul1 = `$${nom[1] + nom[2]}\\\\times\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul2 = `$${nom[1] + nom[2]}\\\\times\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul3 = `$\\\\dfrac{${nom[1] + nom[2]}}{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul4 = `$\\\\dfrac{${nom[1] + nom[2]}}{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul5 = `$\\\\dfrac{${nom[1] + nom[2]}}{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calculTrue = 0\n break\n case 'sinus':\n texteCorr += `In the right triangle $${nom}$ in $${nom[0]}$,<br> the sine of the angle $\\\\widehat{${nom}}$ is defined by:<br>`\n texteCorr += `$\\\\sin \\\\left(\\\\widehat{${nom}}\\\\right)=${deprecatedTexFraction(nom[0] + nom[2], nom[1] + nom[2])}$<br>`\n texteCorr += 'With digital data:<br>'\n texteCorr += `$\\\\dfrac{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}{\\\\color{red}{1}} = ${deprecatedTexFraction(nom[0] + nom[2], bc)}$<br>`\n texteCorr += `${texteEnCouleurEtGras('The cross products are equal, therefore: ', 'red')}<br>`\n texteCorr += `$${nom[0] + nom[2]} = ${quatriemeProportionnelle('\\\\color{red}{1}', bc, `\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)`)}$`\n texteCorr += `i.e. $${nom[0] + nom[2]}\\\\approx${texNombre(ac, 1)}$ ${unite}.`\n reponse = ac.toDP(1)\n nomLongueur = `$${nom[0] + nom[2]}$`\n calcul0 = `$${nom[1] + nom[2]}\\\\times\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul1 = `$${nom[1] + nom[2]}\\\\times\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul2 = `$${nom[1] + nom[2]}\\\\times\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul3 = `$\\\\dfrac{${nom[1] + nom[2]}}{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul4 = `$\\\\dfrac{${nom[1] + nom[2]}}{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul5 = `$\\\\dfrac{${nom[1] + nom[2]}}{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calculTrue = 1\n break\n case 'tangent':\n texteCorr += `In the right triangle $${nom}$ in $${nom[0]}$,<br> the tangent of the angle $\\\\widehat{${nom}}$ is defined by:<br>`\n texteCorr += `$\\\\tan \\\\left(\\\\widehat{${nom}}\\\\right)=${deprecatedTexFraction(nom[0] + nom[2], nom[0] + nom[1])}$<br>`\n texteCorr += 'With digital data:<br>'\n texteCorr += `$\\\\dfrac{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}{\\\\color{red}{1}} = ${deprecatedTexFraction(nom[0] + nom[2], ab)}$<br>`\n texteCorr += `${texteEnCouleurEtGras('The cross products are equal, therefore: ', 'red')}<br>`\n texteCorr += `$${nom[0] + nom[2]} = ${quatriemeProportionnelle('\\\\color{red}{1}', ab, `\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)`)}$`\n texteCorr += `i.e. $${nom[0] + nom[2]}\\\\approx${texNombre(ac, 1)}$ ${unite}.`\n reponse = ac.toDP(1)\n nomLongueur = `$${nom[0] + nom[2]}$`\n calcul0 = `$${nom[0] + nom[1]}\\\\times\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul1 = `$${nom[0] + nom[1]}\\\\times\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul2 = `$${nom[0] + nom[1]}\\\\times\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul3 = `$\\\\dfrac{${nom[0] + nom[1]}}{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul4 = `$\\\\dfrac{${nom[0] + nom[1]}}{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul5 = `$\\\\dfrac{${nom[0] + nom[1]}}{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calculTrue = 2\n break\n case 'invCosine':\n texteCorr += `In the right triangle $${nom}$ in $${nom[0]}$,<br> the cosine of the angle $\\\\widehat{${nom}}$ is defined by:<br>`\n texteCorr += `$\\\\cos\\\\left(\\\\widehat{${nom}}\\\\right)=\\\\dfrac{${nom[0] + nom[1]}}{${nom[1] + nom[2]}}$.<br>`\n texteCorr += 'With digital data:<br>'\n texteCorr += `$\\\\dfrac{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}{\\\\color{red}{1}} = ${deprecatedTexFraction(ab, nom[1] + nom[2])}$<br>`\n texteCorr += `${texteEnCouleurEtGras('The cross products are equal, therefore: ', 'red')}<br>`\n texteCorr += `$${nom[1] + nom[2]} = ${quatriemeProportionnelle(`\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)`, ab, '\\\\color{red}{1}')}$`\n texteCorr += `i.e. $${nom[1] + nom[2]}\\\\approx${texNombre(bc, 1)}$ ${unite}.`\n reponse = bc.toDP(1)\n nomLongueur = `$${nom[1] + nom[2]}$`\n calcul0 = `$${nom[0] + nom[1]}\\\\times\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul1 = `$${nom[0] + nom[1]}\\\\times\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul2 = `$${nom[0] + nom[1]}\\\\times\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul3 = `$\\\\dfrac{${nom[0] + nom[1]}}{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul4 = `$\\\\dfrac{${nom[0] + nom[1]}}{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul5 = `$\\\\dfrac{${nom[0] + nom[1]}}{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calculTrue = 3\n break\n case 'invSinus':\n texteCorr += `In the right triangle $${nom}$ in $${nom[0]}$,<br> the sine of the angle $\\\\widehat{${nom}}$ is defined by:<br>`\n texteCorr += `$\\\\sin \\\\left(\\\\widehat{${nom}}\\\\right)=${deprecatedTexFraction(nom[0] + nom[2], nom[1] + nom[2])}$<br>`\n texteCorr += 'With digital data:<br>'\n texteCorr += `$\\\\dfrac{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}{\\\\color{red}{1}} = ${deprecatedTexFraction(ac, nom[1] + nom[2])}$<br>`\n texteCorr += `${texteEnCouleurEtGras('The cross products are equal, therefore: ', 'red')}<br>`\n texteCorr += `$${nom[1] + nom[2]} = ${quatriemeProportionnelle(`\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)`, ac, '\\\\color{red}{1}')}$`\n texteCorr += `i.e. $${nom[1] + nom[2]}\\\\approx${texNombre(bc, 1)}$ ${unite}.`\n reponse = bc.toDP(1)\n nomLongueur = `$${nom[1] + nom[2]}$`\n calcul0 = `$${nom[0] + nom[2]}\\\\times\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul1 = `$${nom[0] + nom[2]}\\\\times\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul2 = `$${nom[0] + nom[2]}\\\\times\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul3 = `$\\\\dfrac{${nom[0] + nom[2]}}{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul4 = `$\\\\dfrac{${nom[0] + nom[2]}}{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul5 = `$\\\\dfrac{${nom[0] + nom[2]}}{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calculTrue = 4\n break\n case 'invTangent':\n texteCorr += `In the right triangle $${nom}$ in $${nom[0]}$,<br> the tangent of the angle $\\\\widehat{${nom}}$ is defined by:<br>`\n texteCorr += `$\\\\tan \\\\left(\\\\widehat{${nom}}\\\\right)=${deprecatedTexFraction(nom[0] + nom[2], nom[0] + nom[1])}$<br>`\n texteCorr += 'With digital data:<br>'\n texteCorr += `$\\\\dfrac{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}{\\\\color{red}{1}} = ${deprecatedTexFraction(ac, nom[0] + nom[1])}$<br>`\n texteCorr += `${texteEnCouleurEtGras('The cross products are equal, therefore: ', 'red')}<br>`\n texteCorr += `$${nom[0] + nom[1]} = ${quatriemeProportionnelle(`\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)`, ac, '\\\\color{red}{1}')}$`\n texteCorr += `i.e. $${nom[0] + nom[1]}\\\\approx${texNombre(ab, 1)}$ ${unite}.`\n reponse = ab.toDP(1)\n nomLongueur = `$${nom[0] + nom[1]}$`\n calcul0 = `$${nom[0] + nom[2]}\\\\times\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul1 = `$${nom[0] + nom[2]}\\\\times\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul2 = `$${nom[0] + nom[2]}\\\\times\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)$`\n calcul3 = `$\\\\dfrac{${nom[0] + nom[2]}}{\\\\cos\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul4 = `$\\\\dfrac{${nom[0] + nom[2]}}{\\\\sin\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calcul5 = `$\\\\dfrac{${nom[0] + nom[2]}}{\\\\tan\\\\left(${angleABC}\\\\degree\\\\right)}$`\n calculTrue = 5\n break\n }\n if (!context.isHtml && this.correctionDetaillee) {\n texteCorr += '\\n\\\\end{minipage}\\n'\n }\n /*****************************************************/\n // For AMC\n if (context.isAmc) {\n this.autoCorrection[i] = {\n enonce: texteAMC + (this.sup ? mathalea2d(paramsEnonce, objetsEnonce) + '<br>The figure above does not respect the dimensions.' : ''), // + '\\\\\\\\\\n',\n enonceAvantUneFois: true,\n // enounceAfterNumQuestion: true,\n options: {\n multicols: false,\n barreseparation: true,\n multicolsAll: true,\n numerotationEnonce: true\n },\n propositions: [\n {\n type: 'mthMono',\n enonce: numAlpha(0) + `What calculation should be made to calculate ${nomLongueur}?`, // \\\\\\\\\\n`,\n options: {\n ordered: true\n },\n propositions: [\n {\n texte: calcul0,\n statut: calculTrue === 0,\n feedback: ''\n },\n {\n texte: calcul1,\n statut: calculTrue === 1,\n feedback: ''\n },\n {\n texte: calcul2,\n statut: calculTrue === 2,\n feedback: ''\n },\n {\n texte: calcul3,\n statut: calculTrue === 3,\n feedback: ''\n },\n {\n texte: calcul4,\n statut: calculTrue === 4,\n feedback: ''\n },\n {\n texte: calcul5,\n statut: calculTrue === 5,\n feedback: ''\n }\n ]\n },\n {\n type: 'AMCNum',\n propositions: [\n {\n reponse: {\n texte: numAlpha(1) + q2AMC, // `${nomLongueur} rounded to the tenth of ${unite}:\\\\\\\\\\n`,\n valeur: [reponse],\n param: {\n digits: 3,\n decimals: 1,\n signe: false,\n exposantNbChiffres: 0,\n exposantSigne: false,\n approx: 1\n }\n }\n }]\n }\n ]\n }\n }\n if (context.isHtml && !context.isAmc) {\n texte += ajouteChampTexteMathLive(this, i, 'width25 inline units[Length]')\n setReponse(this, i, new Grandeur(reponse, unite), { formatInteractif: 'units' })\n }\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n }\n listeQuestionsToContenu(this) // On envoie l'exercice à la fonction de mise en page\n }\n\n this.besoinFormulaireCaseACocher = ['Freehand Figure', 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