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\begin{document}

\sloppy

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

 Dans le triangle WLP rectangle en W, on sait que :
\begin{itemize}
\item WP=5,6 cm
\item LP=8,7 cm
\end{itemize}

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

 Dans le triangle GNM rectangle en G, on sait que :
\begin{itemize}
\item GN=9,8 cm
\item \(\widehat{NMG}\) =  11\textdegree{}
\end{itemize}

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

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

 Dans le triangle VAJ rectangle en V, on sait que :
\begin{itemize}
\item AJ=4,1 cm
\item \(\widehat{VAJ}\) = 73\textdegree{}
\end{itemize}

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

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

 Dans le triangle MFC rectangle en M, on sait que :
\begin{itemize}
\item MC=5,6 cm
\item FC=8,2 cm
\end{itemize}

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

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

 Dans le triangle FMA rectangle en F, on sait que :
\begin{itemize}
\item FM=1,3 cm
\item \(\widehat{FMA}\) = 63\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [FA]. (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 (2.551,2.707) {?};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{WLP}\)) =  \(\dfrac{WP}{LP}\)
\par\addvspace{.5em}
 d'où sin(\(\widehat{WLP}\)) = \(\dfrac{5{,}6}{8{,}7}\)
\par\addvspace{.5em}
On a donc \(\widehat{WLP}\) =  ArcSin(\(\dfrac{5{,}6}{8{,}7}\)) \(\approx\) 40\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{GMN}\)) = \(\dfrac{GN}{NM}\)
\par\addvspace{.5em}
 D'où sin(11\textdegree{}) = \(\dfrac{9{,}8}{NM}\)
\par\addvspace{.5em}
On a donc NM =\(\dfrac{9{,}8}{\sin(11^{\circ})}\) \(\approx\) 51,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

cos(\(\widehat{VAJ}\)) = \(\dfrac{VA}{AJ}\)
\par\addvspace{.5em}
d'où cos(73\textdegree{}) = \(\dfrac{VA}{4{,}1}\)

On a donc VA = 4,1 \(\times\) cos(73\textdegree{}) \(\approx\) 1,2 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (4.197,0.799) {?};
\end{tikzpicture}\end{center}


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

cos(\(\widehat{MCF}\)) = \(\dfrac{MC}{FC}\)
\par\addvspace{.5em}
  d'où    cos(\(\widehat{MCF}\)) =  \(\dfrac{5{,}6}{8{,}2}\)
\par\addvspace{.5em}
On a donc \(\widehat{MCF}\) = Arccos (\(\dfrac{5{,}6}{8{,}2}\)) \(\approx\) 47\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.500,0.418) {?};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (1.398,2.613) {63°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{FMA}\)) = \(\dfrac{FA}{FM}\)
\par\addvspace{.5em}
d'où tan(63\textdegree{}) =\(\dfrac{FA}{1{,}3}\)
\par\addvspace{.5em}
On a donc FA = 1,3 \(\times\) tan(63\textdegree{}) \(\approx\) 2,6 cm\end{document}
