import work from year 2015-2016
This commit is contained in:
Benjamin Bertrand
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3e/Geometrie/Angle_Centre/exo_angle_centre.pdf
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3e/Geometrie/Angle_Centre/exo_angle_centre.pdf
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3e/Geometrie/Angle_Centre/exo_angle_centre.tex
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3e/Geometrie/Angle_Centre/exo_angle_centre.tex
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\documentclass[a4paper,12pt, twocolumn, landscape]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
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% Title Page
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\titre{Angle au centre - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Avril 2016}
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\pagestyle{empty}
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\begin{document}
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\begin{Exo}
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$A$ et $B$ deux points tels que $AB = 5cm$. $\mathcal{C}$ un cercle de diamètre $[AB]$ et de centre $I$.
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$P$ et $Q$ deux points du cercle $\mathcal{C}$ tels que $\widehat{AQP} = 35^{o}$.
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\begin{enumerate}
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\item Déterminer la mesure de l'angle $\widehat{ABP}$.
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\item Quelle est la nature du triangle $ABP$?
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\item Calculer la longueur de $[AP]$ arrondie au mullimètre.
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\item Déterminer la mesure de l'angle $\widehat{PIB}$.
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\end{enumerate}
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\end{Exo}
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\begin{Exo}
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La figure ci-dessous représente un \textbf{décagone} régulier (c'est un polygone régulier) inscrit dans un cercle $\mathcal{C}$ de centre $O$.
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\begin{center}
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\includegraphics[scale=0.6]{./fig/decagone}
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\end{center}
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\begin{enumerate}
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\item Quel est le nombre de côtés d'un décagone?
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\item Quel est la mesure de l'angle au centre $\widehat{COK}$?
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\item En déduire la mesure de l'angle $\widehat{CEK}$.
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\item Construire une décagone de rayon 5cm.
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\item Quel est la mesure de l'angle $\widehat{IEJ}$?
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\end{enumerate}
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\end{Exo}
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\setcounter{exo}{0}
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\pagebreak
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\begin{Exo}
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$A$ et $B$ deux points tels que $AB = 5cm$. $\mathcal{C}$ un cercle de diamètre $[AB]$ et de centre $I$.
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$P$ et $Q$ deux points du cercle $\mathcal{C}$ tels que $\widehat{AQP} = 35^{o}$.
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||||
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\begin{enumerate}
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\item Déterminer la mesure de l'angle $\widehat{ABP}$.
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\item Quelle est la nature du triangle $ABP$?
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\item Calculer la longueur de $[AP]$ arrondie au mullimètre.
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\item Déterminer la mesure de l'angle $\widehat{PIB}$.
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\end{enumerate}
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\end{Exo}
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\begin{Exo}
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La figure ci-dessous représente un \textbf{décagone} régulier (c'est un polygone régulier) inscrit dans un cercle $\mathcal{C}$ de centre $O$.
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\begin{center}
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\includegraphics[scale=0.6]{./fig/decagone}
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\end{center}
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\begin{enumerate}
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\item Quel est le nombre de côtés d'un décagone?
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\item Quel est la mesure de l'angle au centre $\widehat{COK}$?
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\item En déduire la mesure de l'angle $\widehat{CEK}$.
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\item Construire une décagone de rayon 5cm.
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\item Quel est la mesure de l'angle $\widehat{IEJ}$?
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\end{enumerate}
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\end{Exo}
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\pagebreak
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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3e/Geometrie/Angle_Centre/exo_brevet.pdf
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3e/Geometrie/Angle_Centre/exo_brevet.pdf
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3e/Geometrie/Angle_Centre/exo_brevet.tex
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3e/Geometrie/Angle_Centre/exo_brevet.tex
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
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% Title Page
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\titre{Angle au centre - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Avril 2016}
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\pagestyle{empty}
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\begin{document}
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\begin{Exo}
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\begin{enumerate}
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\item Trace le cercle $\mathcal{C}$ de centre O et de diamètre [AB] tel que AB = 8~cm.
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\item Place un point M appartenant à $\mathcal{C}$ tel que $\widehat{\text{BOM}} = 36$\,\degres.
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\item Calcule la mesure de l'angle inscrit $\widehat{\text{MAB}}$ qui intercepte le petit arc de cercle $\widearc{\text{MB}}$.
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\item À l'aide des données de l'énoncé, laquelle de ces propositions te permet de montrer que AMB est un triangle rectangle en M : (Recopie sur ta copie la bonne proposition)
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\medskip
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\textbf{Proposition 1 :}
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Si dans le triangle AME on a AB$^2$= AM$^2$ + BM$^2$ alors AME est un triangle rectangle en M.
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\textbf{Proposition 2 :}
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Si le triangle AMB est inscrit dans le cercle $\mathcal{C}$ dont l'un des diamètres est [AB] alors AMB est un triangle rectangle en M
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\textbf{Proposition 3 :}
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Si O est le milieu de [AB] alors AMB est un triangle rectangle d'hypoténuse [AB].
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\item Calcule la longueur AM et arrondis le résultat au dixième.
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\item Trace le symétrique N de M par rapport à [AB].
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\item Place les points R et S de façon à ce que NMRAS soit un pentagone régulier.
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\end{enumerate}
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\end{Exo}
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\setcounter{exo}{0}
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\begin{Exo}
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\begin{enumerate}
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\item Trace le cercle $\mathcal{C}$ de centre O et de diamètre [AB] tel que AB = 8~cm.
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\item Place un point M appartenant à $\mathcal{C}$ tel que $\widehat{\text{BOM}} = 36$\,\degres.
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\item Calcule la mesure de l'angle inscrit $\widehat{\text{MAB}}$ qui intercepte le petit arc de cercle $\widearc{\text{MB}}$.
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\item À l'aide des données de l'énoncé, laquelle de ces propositions te permet de montrer que AMB est un triangle rectangle en M : (Recopie sur ta copie la bonne proposition)
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\medskip
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\textbf{Proposition 1 :}
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Si dans le triangle AME on a AB$^2$= AM$^2$ + BM$^2$ alors AME est un triangle rectangle en M.
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\textbf{Proposition 2 :}
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Si le triangle AMB est inscrit dans le cercle $\mathcal{C}$ dont l'un des diamètres est [AB] alors AMB est un triangle rectangle en M
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\textbf{Proposition 3 :}
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Si O est le milieu de [AB] alors AMB est un triangle rectangle d'hypoténuse [AB].
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\item Calcule la longueur AM et arrondis le résultat au dixième.
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\item Trace le symétrique N de M par rapport à [AB].
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\item Place les points R et S de façon à ce que NMRAS soit un pentagone régulier.
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\end{enumerate}
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\end{Exo}
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\setcounter{exo}{0}
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\begin{Exo}
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\begin{enumerate}
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\item Trace le cercle $\mathcal{C}$ de centre O et de diamètre [AB] tel que AB = 8~cm.
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\item Place un point M appartenant à $\mathcal{C}$ tel que $\widehat{\text{BOM}} = 36$\,\degres.
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\item Calcule la mesure de l'angle inscrit $\widehat{\text{MAB}}$ qui intercepte le petit arc de cercle $\widearc{\text{MB}}$.
|
||||
\item À l'aide des données de l'énoncé, laquelle de ces propositions te permet de montrer que AMB est un triangle rectangle en M : (Recopie sur ta copie la bonne proposition)
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\medskip
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\textbf{Proposition 1 :}
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Si dans le triangle AME on a AB$^2$= AM$^2$ + BM$^2$ alors AME est un triangle rectangle en M.
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\textbf{Proposition 2 :}
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Si le triangle AMB est inscrit dans le cercle $\mathcal{C}$ dont l'un des diamètres est [AB] alors AMB est un triangle rectangle en M
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\textbf{Proposition 3 :}
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Si O est le milieu de [AB] alors AMB est un triangle rectangle d'hypoténuse [AB].
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\item Calcule la longueur AM et arrondis le résultat au dixième.
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\item Trace le symétrique N de M par rapport à [AB].
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\item Place les points R et S de façon à ce que NMRAS soit un pentagone régulier.
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\end{enumerate}
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\end{Exo}
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\setcounter{exo}{0}
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\end{document}
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%%% Local Variables:
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||||
%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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3e/Geometrie/Angle_Centre/fig/decagone.pdf
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41
3e/Geometrie/Reciproques/index.rst
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41
3e/Geometrie/Reciproques/index.rst
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@@ -0,0 +1,41 @@
|
||||
Notes autour des théorèmes de Pythagore et de Thalès pour les 3e
|
||||
################################################################
|
||||
|
||||
:date: 2016-01-25
|
||||
:modified: 2016-01-25
|
||||
:tags: Geometrie
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre autour des théorème de Pythagore et de Thalès et leurs réciproques pour les 3e.
|
||||
|
||||
Compétences du programme visée
|
||||
==============================
|
||||
|
||||
- Utiliser le théorème de Thalès pour calculer une longueur
|
||||
- Utiliser le théorème de Thalès pour démontrer le parallélisme
|
||||
- (S) Utiliser le théorème de Pythagore pour calculer une longueur
|
||||
- (S) Utiliser le théorème de Pythagore pour démontrer qu'un triangle est rectangle
|
||||
|
||||
|
||||
Déroulement
|
||||
===========
|
||||
|
||||
Séance 1
|
||||
---------
|
||||
|
||||
Reconstruction du théorème de Pythagore avec les élèves. Quelques exercices basiques.
|
||||
|
||||
Séance 2
|
||||
--------
|
||||
|
||||
Redécouverte de la notion de réciproque à travers la réciproque du théorème de Pythagore.
|
||||
|
||||
Séance 3
|
||||
--------
|
||||
|
||||
Construction de la (les?) réciproques de Thalès. Travail autour de la notion de réciproque.
|
||||
|
||||
Séance 4
|
||||
--------
|
||||
|
||||
Travail technique autour de ces théorèmes. Ce travail sera ensuite repris dans la durée.
|
||||
BIN
3e/Geometrie/Thales_agrandissement/Exo/fig/ombre_pise.pdf
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BIN
3e/Geometrie/Thales_agrandissement/Exo/fig/ombre_pise.pdf
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Binary file not shown.
BIN
3e/Geometrie/Thales_agrandissement/Exo/pise_agrandissement.pdf
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BIN
3e/Geometrie/Thales_agrandissement/Exo/pise_agrandissement.pdf
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117
3e/Geometrie/Thales_agrandissement/Exo/pise_agrandissement.tex
Normal file
117
3e/Geometrie/Thales_agrandissement/Exo/pise_agrandissement.tex
Normal file
@@ -0,0 +1,117 @@
|
||||
\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
|
||||
|
||||
% Title Page
|
||||
\titre{Thalès et agrandissement - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Troisième}
|
||||
\date{Novembre 2015}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Construit un parallélogramme $RAVI$ tel que $RA = 6cm$, $IV = 4cm$ et $\widehat{RIV} = 130^{o}$.
|
||||
\item Construit un agrandissement de rapport $\dfrac{5}{4}$ du parallélogramme $RAVI$.
|
||||
\item Quel est la nature de la figure obtenue?
|
||||
\item En déduire la mesure des angles de la figure agrandie.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Inspiré par l'expérience de Thalès, Tom en voyage à Pise veut mesurer la tour penchée grâce à son ombre. Il se renseigne et apprend qu'elle est penchée de $4,19^o$ comme sur le dessin suivant:
|
||||
|
||||
\hspace{-1cm}
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\includegraphics[scale=0.3]{./fig/ombre_pise}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.2\textwidth}
|
||||
Une fois le bâton installé, il mesure les distances suivantes:
|
||||
\begin{itemize}
|
||||
\item Diamètre de la tour: 15.5m.
|
||||
\item Taille du baton 1,5m.
|
||||
\item Taille de l'ombre du baton: 2m
|
||||
\item Taille de l'ombre de la tour: 66,95m
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Comment doit-il placer son bâton pour pouvoir appliquer le théorème de Thalès? Dessiner le baton sur le dessin.
|
||||
|
||||
\item Reporter les mesures sur le dessin.
|
||||
\item Calculer la hauteur de la tour de Pise.
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Pour ça pièce de théâtre, le metteur en scène a besoin d'un grand arbre de 4m de haut en ombre chinoise. Pour cela, il possède un un patron miniature de cet arbre mesurant 1m qu'il va éclairé avec une lampe. Cet arbre miniature est fixé à 5m de la toile.
|
||||
\begin{enumerate}
|
||||
\item Faire un schéma résumant l'installation.
|
||||
\item Quel devra être la rapport d'agrandissement?
|
||||
\item À quel du sapin devra-t-on placer la lampe pour que l'ombre du sapin soit de la bonne taille?
|
||||
\end{enumerate}
|
||||
|
||||
|
||||
\end{Exo}
|
||||
|
||||
\setcounter{exo}{0}
|
||||
\pagebreak
|
||||
|
||||
\begin{Exo}
|
||||
\begin{enumerate}
|
||||
\item Construit un parallélogramme $RAVI$ tel que $RA = 6cm$, $IV = 4cm$ et $\widehat{RIV} = 130^{o}$.
|
||||
\item Construit un agrandissement de rapport $\dfrac{5}{4}$ du parallélogramme $RAVI$.
|
||||
\item Quel est la nature de la figure obtenue?
|
||||
\item En déduire la mesure des angles de la figure agrandie.
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}
|
||||
Inspiré par l'expérience de Thalès, Tom en voyage à Pise veut mesurer la tour penchée grâce à son ombre. Il se renseigne et apprend qu'elle est penchée de $4,19^o$ comme sur le dessin suivant:
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\hspace{-1cm}
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\begin{minipage}{0.3\textwidth}
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\includegraphics[scale=0.3]{./fig/ombre_pise}
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\end{minipage}
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\begin{minipage}{0.2\textwidth}
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Une fois le bâton installé, il mesure les distances suivantes:
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\begin{itemize}
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\item Diamètre de la tour: 15.5m.
|
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\item Taille du baton 1,5m.
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\item Taille de l'ombre du baton: 2m
|
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\item Taille de l'ombre de la tour: 66,95m
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\end{itemize}
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\end{minipage}
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\begin{enumerate}
|
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\item Comment doit-il placer son bâton pour pouvoir appliquer le théorème de Thalès? Dessiner le baton sur le dessin.
|
||||
|
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\item Reporter les mesures sur le dessin.
|
||||
\item Calculer la hauteur de la tour de Pise.
|
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\end{enumerate}
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\end{Exo}
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\begin{Exo}
|
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Pour ça pièce de théâtre, le metteur en scène a besoin d'un grand arbre de 4m de haut en ombre chinoise. Pour cela, il possède un un patron miniature de cet arbre mesurant 1m qu'il va éclairé avec une lampe. Cet arbre miniature est fixé à 5m de la toile.
|
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\begin{enumerate}
|
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\item Faire un schéma résumant l'installation.
|
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\item Quel devra être la rapport d'agrandissement?
|
||||
\item À quel du sapin devra-t-on placer la lampe pour que l'ombre du sapin soit de la bonne taille?
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\end{enumerate}
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\end{Exo}
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\pagebreak
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43
3e/Geometrie/Thales_agrandissement/index.rst
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Thalès agrandissement de longueur pour les 3e
|
||||
#############################################
|
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|
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:date: 2015-10-30
|
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:modified: 2015-10-30
|
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:category: 3e
|
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:tags: Géométrie
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Notes sur le premier chapitre autour de Thalès pour les 3e
|
||||
|
||||
Liens externes autour de ce chapitre
|
||||
|
||||
- _AGRANDISSEMENT-RÉDUCTION D'UNE FIGURE: `http://www.apmep.fr/IMG/pdf/AG1.pdf`
|
||||
|
||||
Dans ce chapitre on mène de front l'activité liée au dessus et un cours classique autour de Thalès.
|
||||
|
||||
Séquence 1
|
||||
==========
|
||||
|
||||
Énoncé du théorème de Thalès (version tableau de proportionnalité) et un exemple.
|
||||
|
||||
Exercices techniques autour du théorème de Thalès (pour calculer des longueurs)
|
||||
|
||||
Séquence 2
|
||||
==========
|
||||
|
||||
Projection des images pour définir ce que l'on entend par agrandissement et réduction.
|
||||
|
||||
Exercices techniques autour du théorème de Thalès (pour calculer des longueurs)
|
||||
|
||||
Séquence 3
|
||||
==========
|
||||
|
||||
Figures à découper pour découvrir des "familles" de figures agrandis ou réduites.
|
||||
|
||||
Exercices techniques autour du théorème de Thalès (pour calculer des longueurs)
|
||||
|
||||
Séquence 4
|
||||
==========
|
||||
|
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Cours autour de l'agrandissement.
|
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|
||||
Exercices autour de Thalès et de l'agrandissement.
|
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86
3e/Geometrie/Trigonometrie/index.rst
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86
3e/Geometrie/Trigonometrie/index.rst
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|
||||
Notes sur le chapitre de trigonométrie pour les 3e
|
||||
##################################################
|
||||
|
||||
:date: 2016-03-18
|
||||
:modified: 2016-03-14
|
||||
:tags: Trigonometrie, Geometrie
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur la trigonométrie pour les 3e.
|
||||
|
||||
Objectif du programme
|
||||
=====================
|
||||
|
||||
- Connaître les relations entre deux côtés et un angle d'un triangle rectangle
|
||||
- Déterminer à la calculatrice la mesure d'un angle à partir de deux côtés
|
||||
- Déterminer à la calculatrice la longueur d'un côté à partir d'un autre et d'un angle
|
||||
|
||||
Cours
|
||||
=====
|
||||
|
||||
Bilan sur Pythagore et cadre et objectif du chapitre.
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Pythagore:
|
||||
|
||||
2 longueur -> la 3e longueur.
|
||||
|
||||
Trigonométrie:
|
||||
|
||||
2 longueur -> un angle
|
||||
1 longueur et un angle -> les autres longueurs
|
||||
|
||||
Vocabulaire du triangle
|
||||
~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Sur une figure:
|
||||
|
||||
- Angle
|
||||
- Hypoténuse
|
||||
- Opposé
|
||||
- Adjacent
|
||||
|
||||
Formules trigonométriques
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Les formules ainsi que 2 exemples pour le calcul de longueur et d'angle.
|
||||
|
||||
Déroulement
|
||||
===========
|
||||
|
||||
Séance 1
|
||||
~~~~~~~~
|
||||
|
||||
Objectif et vocabulaire du triangle.
|
||||
|
||||
Fiche avec les mesures sud les triangles.
|
||||
|
||||
Séance 2
|
||||
~~~~~~~~
|
||||
|
||||
Cours: les 3 formules
|
||||
|
||||
Calculer une longueur à partir d'un angle et d'une longueur.
|
||||
|
||||
Séance 3
|
||||
~~~~~~~~
|
||||
|
||||
Correction du premier exercice (à finir à la maison).
|
||||
Exercice 2 de la fiche.
|
||||
|
||||
Un exemple de calcul d'un angle.
|
||||
|
||||
|
||||
Séance 4
|
||||
~~~~~~~~
|
||||
|
||||
Calcul d'un angle à partir de deux longueurs.
|
||||
|
||||
Idées situations exercices
|
||||
==========================
|
||||
|
||||
- Longueur de plage recouverte par la marée (Brevet des collèges Nouvelle-Calédonie, 11 décembre 2012)
|
||||
- Profondeur de l'ancre avec du courant
|
||||
- Pente en ski
|
||||
- Triangulation navigation (Brevet Nouvelle-Calédonie, 6 décembre 2011)
|
||||
|
||||
BIN
3e/Geometrie/Trigonometrie/intro_trigo.pdf
Normal file
BIN
3e/Geometrie/Trigonometrie/intro_trigo.pdf
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Binary file not shown.
88
3e/Geometrie/Trigonometrie/intro_trigo.tex
Normal file
88
3e/Geometrie/Trigonometrie/intro_trigo.tex
Normal file
@@ -0,0 +1,88 @@
|
||||
\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
|
||||
|
||||
% Title Page
|
||||
\titre{Introduction à la trigonométrie}
|
||||
\classe{Troisième}
|
||||
\date{mars 2014}
|
||||
|
||||
\pagestyle{empty}
|
||||
\geometry{left=5mm,right=5mm, bottom= 10mm, top=10mm}
|
||||
|
||||
\begin{document}
|
||||
|
||||
|
||||
Compléter le tableau suivant en fonction des triangles.
|
||||
|
||||
\begin{tabular}{|c|*{6}{c|}}
|
||||
\hline
|
||||
Triangle & Hypoténuse & coté adjacent & coté opposé & angle & $\frac{\mbox{coté adjacent}}{\mbox{Hypoténuse}}$ & $\frac{\mbox{coté opposé}}{\mbox{Hypoténuse}}$ \\
|
||||
\hline
|
||||
ABC & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
DEF & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
GHI & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
JKL & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
MNP & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.4]{./fig/triangles}
|
||||
\end{center}
|
||||
|
||||
\begin{Exo}
|
||||
|
||||
\textbf{Avec la figure suivante, calculer la longueur $BA$.}
|
||||
\\[0.3cm]
|
||||
|
||||
\begin{minipage}[h]{0.2\textwidth}
|
||||
\includegraphics[scale=0.15]{./fig/triangleABC}
|
||||
\end{minipage}
|
||||
\begin{minipage}[h]{0.8\textwidth}
|
||||
\textit{Questions à se poser}
|
||||
\begin{itemize}
|
||||
\item On connait
|
||||
\begin{center}
|
||||
hypoténuse\hspace{0.5cm} opposé \hspace{0.5cm}adjacent \hspace{0.5cm}angle
|
||||
\end{center}
|
||||
\item On cherche
|
||||
\begin{center}
|
||||
hypoténuse\hspace{0.5cm} opposé \hspace{0.5cm}adjacent \hspace{0.5cm}angle
|
||||
\end{center}
|
||||
\end{itemize}
|
||||
\begin{itemize}
|
||||
\item On utilise la formule
|
||||
\begin{eqnarray*}
|
||||
\cos( \widehat{BAC}) = \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.5cm}
|
||||
\sin( \widehat{BAC}) = \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.5cm}
|
||||
\tan( \widehat{BAC}) = \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
\textit{Rédaction:}
|
||||
|
||||
\noindent\fbox{\parbox{\linewidth-2\fboxrule-2\fboxsep}{
|
||||
.\\
|
||||
\parbox{1cm}{\dotfill} est un triangle rectangle en \parbox{0.5cm}{\dotfill} donc
|
||||
\begin{eqnarray*}
|
||||
\parbox{1cm}{\dotfill}(\widehat{BAC}) &=& \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.7cm} \textit{(avec les lettres)}\\[0.3cm]
|
||||
\parbox{1cm}{\dotfill}(\parbox{1cm}{\dotfill}) &=& \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.7cm} \textit{(avec les chiffres)} \\[0.3cm]
|
||||
\parbox{1cm}{\dotfill} &=& \frac{\parbox{2cm}{\dotfill}}{\parbox{2cm}{\dotfill}} \hspace{0.7cm} \textit{(avec les chiffres)} \\[0.3cm]
|
||||
BA & = & \parbox{1cm}{\dotfill} \times \parbox{1cm}{\dotfill} = \parbox{1cm}{\dotfill}
|
||||
\end{eqnarray*}
|
||||
Donc $BA = \parbox{1cm}{\dotfill}$
|
||||
}}
|
||||
\end{Exo}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Reference in New Issue
Block a user