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\begin{document}

\sloppy

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

 Dans le triangle ZGA rectangle en Z, on sait que :
\begin{itemize}
\item ZG=2,5 cm
\item GA=8,2 cm
\end{itemize}

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

 Dans le triangle VRS rectangle en V, on sait que :
\begin{itemize}
\item VS=3,7 cm
\item \(\widehat{RSV}\) =  14\textdegree{}
\end{itemize}

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

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

 Dans le triangle AJV rectangle en A, on sait que :
\begin{itemize}
\item AJ=2,7 cm
\item AV=5,2 cm
\end{itemize}

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

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

 Dans le triangle ZPW rectangle en Z, on sait que :
\begin{itemize}
\item ZP=3,9 cm
\item \(\widehat{PWZ}\) =  40\textdegree{}
\end{itemize}

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

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

 Dans le triangle PLM rectangle en P, on sait que :
\begin{itemize}
\item PL=6,3 cm
\item \(\widehat{PLM}\) = 48\textdegree{}
\end{itemize}

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

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

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

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

cos(\(\widehat{ZGA}\)) = \(\dfrac{ZG}{GA}\)
\par\addvspace{.5em}
 d'où cos(\(\widehat{ZGA}\)) = \(\dfrac{2{,}5}{8{,}2}\)
\par\addvspace{.5em}
On a donc \(\widehat{ZGA}\) =ArcCos(\(\dfrac{2{,}5}{8{,}2}\)) \(\approx\)72\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
tan(\(\widehat{VSR}\)) = \(\dfrac{VR}{VS}\)
\par\addvspace{.5em}
d'où  tan(14\textdegree{}) =  \(\dfrac{VR}{3{,}7}\)
\par\addvspace{.5em}
On a donc VR =  3,7 \(\times\) tan(14\textdegree{})  \(\approx\) 0,9 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{AVJ}\)) = \(\dfrac{AJ}{AV}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{AVJ}\)) =  \(\dfrac{2{,}7}{5{,}2}\)
\par\addvspace{.5em}
 On a donc \(\widehat{AVJ}\) =  ArcTan(\(\dfrac{2{,}7}{5{,}2}\)) \(\approx\) 27\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (4.542,0.761) {40°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{ZWP}\)) = \(\dfrac{ZP}{ZW}\)
\par\addvspace{.5em}
d'où  tan(40\textdegree{}) =  \(\dfrac{3{,}9}{ZW}\)
\par\addvspace{.5em}
On a donc ZW = \(\dfrac{3{,}9}{\tan(40^{\circ})}\) \(\approx\) 4,6 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \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 (2.216,2.724) {48°};
\end{tikzpicture}\end{center}


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

cos(\(\widehat{PLM}\)) = \(\dfrac{PL}{LM}\)
\par\addvspace{.5em}
 d'où cos(48\textdegree{}) = \(\dfrac{6{,}3}{LM}\)
\par\addvspace{.5em}
On a donc LM = \(\dfrac{6{,}3}{\cos(48^{\circ})}\)\(\approx\) 9,4 cm\end{document}
