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\begin{document}

\sloppy

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

 Dans le triangle AZF rectangle en A, on sait que :
\begin{itemize}
\item AF=2,6 cm
\item \(\widehat{AZF}\) = 57\textdegree{}
\end{itemize}

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

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

 Dans le triangle AWH rectangle en A, on sait que :
\begin{itemize}
\item AW=2,2 cm
\item WH=8,5 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{AWH}\).
\needspace{4\baselineskip}
\section*{
Exercice 3}

 Dans le triangle GJD rectangle en G, on sait que :
\begin{itemize}
\item GJ=2,1 cm
\item GD=5,3 cm
\end{itemize}

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

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

 Dans le triangle TZC rectangle en T, on sait que :
\begin{itemize}
\item ZC=10 cm
\item \(\widehat{TZC}\) = 63\textdegree{}
\end{itemize}

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

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

 Dans le triangle VNS rectangle en V, on sait que :
\begin{itemize}
\item VN=9,5 cm
\item \(\widehat{NSV}\) =  13\textdegree{}
\end{itemize}

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

\newpage
\section*{\textcolor{red}{Correction}}

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

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

\par\addvspace{.5em}
sin(\(\widehat{AZF}\)) =  \(\dfrac{AF}{ZF}\)
\par\addvspace{.5em}
 d'où sin(57\textdegree{}) = \(\dfrac{2{,}6}{ZF}\)
\par\addvspace{.5em}
 On a donc ZF = \(\dfrac{2{,}6}{\sin(57^{\circ})}\) \(\approx\) 3,1 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

cos(\(\widehat{AWH}\)) = \(\dfrac{AW}{WH}\)
\par\addvspace{.5em}
 d'où cos(\(\widehat{AWH}\)) = \(\dfrac{2{,}2}{8{,}5}\)
\par\addvspace{.5em}
On a donc \(\widehat{AWH}\) =ArcCos(\(\dfrac{2{,}2}{8{,}5}\)) \(\approx\)75\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{GDJ}\)) = \(\dfrac{GJ}{GD}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{GDJ}\)) =  \(\dfrac{2{,}1}{5{,}3}\)
\par\addvspace{.5em}
 On a donc \(\widehat{GDJ}\) =  ArcTan(\(\dfrac{2{,}1}{5{,}3}\)) \(\approx\) 22\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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 Dans le triangle TZC rectangle en T, on cherche une relation entre l'angle aigu   \(\widehat{TZC}\) son coté adjacent et l'hypoténuse du triangle.

cos(\(\widehat{TZC}\)) = \(\dfrac{TZ}{ZC}\)
\par\addvspace{.5em}
d'où cos(63\textdegree{}) = \(\dfrac{TZ}{10}\)

On a donc TZ = 10 \(\times\) cos(63\textdegree{}) \(\approx\) 4,5 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (0.550,1.933) {9,5 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.500,1.101) {?};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (5.288,1.443) {13°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{VSN}\)) = \(\dfrac{VN}{VS}\)
\par\addvspace{.5em}
d'où  tan(13\textdegree{}) =  \(\dfrac{9{,}5}{VS}\)
\par\addvspace{.5em}
On a donc VS = \(\dfrac{9{,}5}{\tan(13^{\circ})}\) \(\approx\) 41,1 cm\end{document}
