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\begin{document}

\sloppy

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

 Dans le triangle DPN rectangle en D, on sait que :
\begin{itemize}
\item DP=7,9 cm
\item \(\widehat{PND}\) =  37\textdegree{}
\end{itemize}

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

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

 Dans le triangle VRA rectangle en V, on sait que :
\begin{itemize}
\item VR=1,5 cm
\item RA=7 cm
\end{itemize}

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

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

 Dans le triangle DAR rectangle en D, on sait que :
\begin{itemize}
\item DA=7,8 cm
\item \(\widehat{DAR}\) = 68\textdegree{}
\end{itemize}

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

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

 Dans le triangle JFT rectangle en J, on sait que :
\begin{itemize}
\item JF=1,6 cm
\item JT=5,5 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{JFT}\).
\needspace{4\baselineskip}
\section*{
Exercice 5}

 Dans le triangle ZWG rectangle en Z, on sait que :
\begin{itemize}
\item ZG=9,8 cm
\item \(\widehat{ZWG}\) = 48\textdegree{}
\end{itemize}

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

\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 (4.726,0.745) {37°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{DNP}\)) = \(\dfrac{DP}{DN}\)
\par\addvspace{.5em}
d'où  tan(37\textdegree{}) =  \(\dfrac{7{,}9}{DN}\)
\par\addvspace{.5em}
On a donc DN = \(\dfrac{7{,}9}{\tan(37^{\circ})}\) \(\approx\) 10,5 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{VAR}\)) = \(\dfrac{VR}{RA}\)
\par\addvspace{.5em}
d'où sin(\(\widehat{VAR}\)) =\(\dfrac{1{,}5}{7}\)
\par\addvspace{.5em}
 On a donc \(\widehat{VAR}\) = ArcSin(\(\dfrac{1{,}5}{7}\)) \(\approx\) 12\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

cos(\(\widehat{DAR}\)) = \(\dfrac{DA}{AR}\)
\par\addvspace{.5em}
 d'où cos(68\textdegree{}) = \(\dfrac{7{,}8}{AR}\)
\par\addvspace{.5em}
On a donc AR = \(\dfrac{7{,}8}{\cos(68^{\circ})}\)\(\approx\) 20,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{JFT}\)) = \(\dfrac{JT}{JF}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{JFT}\)) = \(\dfrac{5{,}5}{1{,}6}\)
\par\addvspace{.5em}
 On a donc JFT = ArcTan(\(\dfrac{5{,}5}{1{,}6}\)) \(\approx\) 74\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (2.216,2.724) {48°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{ZWG}\)) = \(\dfrac{ZG}{ZW}\)
\par\addvspace{.5em}
tan(48\textdegree{}) = \(\dfrac{9{,}8}{ZW}\)
\par\addvspace{.5em}
 On a donc ZW = \(\dfrac{9{,}8}{\tan(48^{\circ})}\) \(\approx\) 8,8 cm\end{document}
