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\begin{document}

\sloppy

\needspace{4\baselineskip}
\section*{
Exercice 1}

 Dans le triangle ZCN rectangle en Z, on sait que :
\begin{itemize}
\item CN=8 cm
\item \(\widehat{ZCN}\) = 46\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [ZC]. (Arrondir au dixième)

\needspace{4\baselineskip}
\section*{
Exercice 2}

 Dans le triangle MZT rectangle en M, on sait que :
\begin{itemize}
\item ZT=9,3 cm
\item \(\widehat{MZT}\) = 80\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [MT]. (Arrondir au dixième)

\needspace{4\baselineskip}
\section*{
Exercice 3}

 Dans le triangle GML rectangle en G, on sait que :
\begin{itemize}
\item GM=3,2 cm
\item GL=4,7 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{GLM}\).

\needspace{4\baselineskip}
\section*{
Exercice 4}

 Dans le triangle ZCS rectangle en Z, on sait que :
\begin{itemize}
\item ZS=2,1 cm
\item \(\widehat{CSZ}\) =  30\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [SC]. (Arrondir au dixième)

\needspace{4\baselineskip}
\section*{
Exercice 5}

 Dans le triangle VBD rectangle en V, on sait que :
\begin{itemize}
\item VB=1,3 cm
\item VD=3,9 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{VBD}\). \newpage
\section*{\textcolor{red}{Correction}}

\needspace{4\baselineskip}
\subsection*{
Exercice 1}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (2.311,2.720) {46°};
\end{tikzpicture}\end{center}


 Dans le triangle ZCN rectangle en Z, on cherche une relation entre l'angle aigu   \(\widehat{ZCN}\) son coté adjacent et l'hypoténuse du triangle.

cos(\(\widehat{ZCN}\)) = \(\dfrac{ZC}{CN}\)
\par\addvspace{.5em}
d'où cos(46\textdegree{}) = \(\dfrac{ZC}{8}\)

On a donc ZC = 8 \(\times\) cos(46\textdegree{}) \(\approx\) 5,6 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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 Dans le triangle MZT rectangle en M, on cherche une relation entre l'angle aigu   \(\widehat{MZT}\) son coté opposé et l'hypoténuse du triangle.

\par\addvspace{.5em}
sin(\(\widehat{MZT}\)) =  \(\dfrac{MT}{ZT}\)
\par\addvspace{.5em}
 d'où sin(80\textdegree{}) = \(\dfrac{MT}{9{,}3}\)

On a donc MT = 9,3 \(\times\) sin(80\textdegree{}) \(\approx\) 9,2 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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 Dans le triangle GML rectangle en G, on cherche une relation entre l'angle aigu   \(\widehat{GLM}\) son coté opposé et son coté adjacent.

\par\addvspace{.5em}
tan(\(\widehat{GLM}\)) = \(\dfrac{GM}{GL}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{GLM}\)) =  \(\dfrac{3{,}2}{4{,}7}\)
\par\addvspace{.5em}
 On a donc \(\widehat{GLM}\) =  ArcTan(\(\dfrac{3{,}2}{4{,}7}\)) \(\approx\) 34\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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 Dans le triangle ZCS rectangle en Z, on cherche une relation entre l'angle aigu   \(\widehat{ZSC}\) son coté adjacent et l'hypoténuse du triangle.

cos(\(\widehat{ZSC}\)) = \(\dfrac{ZS}{CS}\)
\par\addvspace{.5em}
  d'où    cos(30\textdegree{}) =  \(\dfrac{2{,}1}{CS}\)
\par\addvspace{.5em}
 On a donc CS =  \(\dfrac{2{,}1}{\cos(30^{\circ})}\) \(\approx\) 2,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.500,0.850) {3,9 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (1.440,2.209) {?};
\end{tikzpicture}\end{center}


 Dans le triangle VBD rectangle en V, on cherche une relation entre l'angle aigu   \(\widehat{VBD}\) son coté adjacent et son coté opposé.

\par\addvspace{.5em}
tan(\(\widehat{VBD}\)) = \(\dfrac{VD}{VB}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{VBD}\)) = \(\dfrac{3{,}9}{1{,}3}\)
\par\addvspace{.5em}
 On a donc VBD = ArcTan(\(\dfrac{3{,}9}{1{,}3}\)) \(\approx\) 72\textdegree{}\end{document}
