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\begin{document}

\sloppy

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

 Dans le triangle RGJ rectangle en R, on sait que :
\begin{itemize}
\item RG=1,8 cm
\item GJ=9,2 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{RGJ}\).
\needspace{4\baselineskip}
\section*{
Exercice 2}

 Dans le triangle ZSC rectangle en Z, on sait que :
\begin{itemize}
\item SC=9,3 cm
\item \(\widehat{SCZ}\) =  20\textdegree{}
\end{itemize}

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

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

 Dans le triangle LRA rectangle en L, on sait que :
\begin{itemize}
\item LR=3,2 cm
\item LA=5,3 cm
\end{itemize}

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

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

 Dans le triangle WGV rectangle en W, on sait que :
\begin{itemize}
\item GV=7,2 cm
\item \(\widehat{GVW}\) =  18\textdegree{}
\end{itemize}

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

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

 Dans le triangle ZNA rectangle en Z, on sait que :
\begin{itemize}
\item ZA=8,5 cm
\item \(\widehat{ZNA}\) = 64\textdegree{}
\end{itemize}

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

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

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

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

cos(\(\widehat{RGJ}\)) = \(\dfrac{RG}{GJ}\)
\par\addvspace{.5em}
 d'où cos(\(\widehat{RGJ}\)) = \(\dfrac{1{,}8}{9{,}2}\)
\par\addvspace{.5em}
On a donc \(\widehat{RGJ}\) =ArcCos(\(\dfrac{1{,}8}{9{,}2}\)) \(\approx\)79\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

cos(\(\widehat{ZCS}\)) = \(\dfrac{ZC}{SC}\)
\par\addvspace{.5em}
  d'où    cos(20\textdegree{}) =  \(\dfrac{ZC}{9{,}3}\)

On a donc ZC = 9,3 \(\times\) cos(20\textdegree{}) \(\approx\) 8{,}7 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
tan(\(\widehat{LAR}\)) = \(\dfrac{LR}{LA}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{LAR}\)) =  \(\dfrac{3{,}2}{5{,}3}\)
\par\addvspace{.5em}
 On a donc \(\widehat{LAR}\) =  ArcTan(\(\dfrac{3{,}2}{5{,}3}\)) \(\approx\) 31\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
sin(\(\widehat{WVG}\)) = \(\dfrac{WG}{GV}\)
\par\addvspace{.5em}
 D'où sin(18\textdegree{}) = \(\dfrac{WG}{7{,}2}\)

On a donc WG = 7,2 \(\times\) sin(18\textdegree{}) \(\approx\) 2,2 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.500,0.472) {8,5 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.667,2.000) {?};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (1.403,2.563) {64°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{ZNA}\)) =  \(\dfrac{ZA}{NA}\)
\par\addvspace{.5em}
 d'où sin(64\textdegree{}) = \(\dfrac{8{,}5}{NA}\)
\par\addvspace{.5em}
 On a donc NA = \(\dfrac{8{,}5}{\sin(64^{\circ})}\) \(\approx\) 9,5 cm\end{document}
