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\begin{document}

\sloppy

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

 Dans le triangle MVB rectangle en M, on sait que :
\begin{itemize}
\item VB=2,2 cm
\item \(\widehat{MVB}\) = 77\textdegree{}
\end{itemize}

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

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

 Dans le triangle TNW rectangle en T, on sait que :
\begin{itemize}
\item TW=6,3 cm
\item NW=8,2 cm
\end{itemize}

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

 Dans le triangle ZHF rectangle en Z, on sait que :
\begin{itemize}
\item ZF=8 cm
\item \(\widehat{HFZ}\) =  36\textdegree{}
\end{itemize}

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

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

 Dans le triangle WCS rectangle en W, on sait que :
\begin{itemize}
\item WC=2,4 cm
\item WS=4,1 cm
\end{itemize}

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

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

 Dans le triangle GLP rectangle en G, on sait que :
\begin{itemize}
\item GP=7,3 cm
\item \(\widehat{GLP}\) = 56\textdegree{}
\end{itemize}

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

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

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

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

\par\addvspace{.5em}
sin(\(\widehat{MVB}\)) =  \(\dfrac{MB}{VB}\)
\par\addvspace{.5em}
 d'où sin(77\textdegree{}) = \(\dfrac{MB}{2{,}2}\)

On a donc MB = 2,2 \(\times\) sin(77\textdegree{}) \(\approx\) 2,1 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{TNW}\)) =  \(\dfrac{TW}{NW}\)
\par\addvspace{.5em}
 d'où sin(\(\widehat{TNW}\)) = \(\dfrac{6{,}3}{8{,}2}\)
\par\addvspace{.5em}
On a donc \(\widehat{TNW}\) =  ArcSin(\(\dfrac{6{,}3}{8{,}2}\)) \(\approx\) 50\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
tan(\(\widehat{ZFH}\)) = \(\dfrac{ZH}{ZF}\)
\par\addvspace{.5em}
d'où  tan(36\textdegree{}) =  \(\dfrac{ZH}{8}\)
\par\addvspace{.5em}
On a donc ZH =  8 \(\times\) tan(36\textdegree{})  \(\approx\) 5,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{WSC}\)) = \(\dfrac{WC}{WS}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{WSC}\)) =  \(\dfrac{2{,}4}{4{,}1}\)
\par\addvspace{.5em}
 On a donc \(\widehat{WSC}\) =  ArcTan(\(\dfrac{2{,}4}{4{,}1}\)) \(\approx\) 30\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (1.737,2.745) {56°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{GLP}\)) =  \(\dfrac{GP}{LP}\)
\par\addvspace{.5em}
 d'où sin(56\textdegree{}) = \(\dfrac{7{,}3}{LP}\)
\par\addvspace{.5em}
 On a donc LP = \(\dfrac{7{,}3}{\sin(56^{\circ})}\) \(\approx\) 8,8 cm\end{document}
