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\begin{document}

\sloppy

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

 Dans le triangle GRW rectangle en G, on sait que :
\begin{itemize}
\item GW=4,3 cm
\item RW=6,7 cm
\end{itemize}

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

 Dans le triangle ZDK rectangle en Z, on sait que :
\begin{itemize}
\item ZD=2,2 cm
\item \(\widehat{DKZ}\) =  37\textdegree{}
\end{itemize}

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

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

 Dans le triangle HSD rectangle en H, on sait que :
\begin{itemize}
\item SD=5,3 cm
\item \(\widehat{HSD}\) = 46\textdegree{}
\end{itemize}

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

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

 Dans le triangle PLG rectangle en P, on sait que :
\begin{itemize}
\item LG=4,3 cm
\item \(\widehat{PLG}\) = 76\textdegree{}
\end{itemize}

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

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

 Dans le triangle FZV rectangle en F, on sait que :
\begin{itemize}
\item FV=5,9 cm
\item ZV=8,5 cm
\end{itemize}

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

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

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

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

\par\addvspace{.5em}
sin(\(\widehat{GRW}\)) =  \(\dfrac{GW}{RW}\)
\par\addvspace{.5em}
 d'où sin(\(\widehat{GRW}\)) = \(\dfrac{4{,}3}{6{,}7}\)
\par\addvspace{.5em}
On a donc \(\widehat{GRW}\) =  ArcSin(\(\dfrac{4{,}3}{6{,}7}\)) \(\approx\) 40\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{ZKD}\)) = \(\dfrac{ZD}{DK}\)
\par\addvspace{.5em}
 D'où sin(37\textdegree{}) = \(\dfrac{2{,}2}{DK}\)
\par\addvspace{.5em}
On a donc DK =\(\dfrac{2{,}2}{\sin(37^{\circ})}\) \(\approx\) 3,7 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
sin(\(\widehat{HSD}\)) =  \(\dfrac{HD}{SD}\)
\par\addvspace{.5em}
 d'où sin(46\textdegree{}) = \(\dfrac{HD}{5{,}3}\)

On a donc HD = 5,3 \(\times\) sin(46\textdegree{}) \(\approx\) 3,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

cos(\(\widehat{PLG}\)) = \(\dfrac{PL}{LG}\)
\par\addvspace{.5em}
d'où cos(76\textdegree{}) = \(\dfrac{PL}{4{,}3}\)

On a donc PL = 4,3 \(\times\) cos(76\textdegree{}) \(\approx\) 1 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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\end{tikzpicture}\end{center}


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

cos(\(\widehat{FVZ}\)) = \(\dfrac{FV}{ZV}\)
\par\addvspace{.5em}
  d'où    cos(\(\widehat{FVZ}\)) =  \(\dfrac{5{,}9}{8{,}5}\)
\par\addvspace{.5em}
On a donc \(\widehat{FVZ}\) = Arccos (\(\dfrac{5{,}9}{8{,}5}\)) \(\approx\) 46\textdegree{} \end{document}
