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\begin{document}

\sloppy

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

 Dans le triangle NWZ rectangle en N, on sait que :
\begin{itemize}
\item NW=1,4 cm
\item NZ=5,5 cm
\end{itemize}

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

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

 Dans le triangle BJV rectangle en B, on sait que :
\begin{itemize}
\item BJ=9,7 cm
\item \(\widehat{BJV}\) = 72\textdegree{}
\end{itemize}

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

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

 Dans le triangle DCF rectangle en D, on sait que :
\begin{itemize}
\item DF=1,1 cm
\item \(\widehat{CFD}\) =  12\textdegree{}
\end{itemize}

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

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

 Dans le triangle LZH rectangle en L, on sait que :
\begin{itemize}
\item ZH=2,4 cm
\item \(\widehat{LZH}\) = 80\textdegree{}
\end{itemize}

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

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

 Dans le triangle WGL rectangle en W, on sait que :
\begin{itemize}
\item WG=3,2 cm
\item GL=8,7 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{WGL}\). \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 (5.289,1.393) {?};
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 Dans le triangle NWZ rectangle en N, on cherche une relation entre l'angle aigu   \(\widehat{NZW}\) son coté opposé et son coté adjacent.

\par\addvspace{.5em}
tan(\(\widehat{NZW}\)) = \(\dfrac{NW}{NZ}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{NZW}\)) =  \(\dfrac{1{,}4}{5{,}5}\)
\par\addvspace{.5em}
 On a donc \(\widehat{NZW}\) =  ArcTan(\(\dfrac{1{,}4}{5{,}5}\)) \(\approx\) 14\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

cos(\(\widehat{BJV}\)) = \(\dfrac{BJ}{JV}\)
\par\addvspace{.5em}
 d'où cos(72\textdegree{}) = \(\dfrac{9{,}7}{JV}\)
\par\addvspace{.5em}
On a donc JV = \(\dfrac{9{,}7}{\cos(72^{\circ})}\)\(\approx\) 31,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (0.550,1.933) {?};
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\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{DFC}\)) = \(\dfrac{DC}{DF}\)
\par\addvspace{.5em}
d'où  tan(12\textdegree{}) =  \(\dfrac{DC}{1{,}1}\)
\par\addvspace{.5em}
On a donc DC =  1,1 \(\times\) tan(12\textdegree{})  \(\approx\) 0,2 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
sin(\(\widehat{LZH}\)) =  \(\dfrac{LH}{ZH}\)
\par\addvspace{.5em}
 d'où sin(80\textdegree{}) = \(\dfrac{LH}{2{,}4}\)

On a donc LH = 2,4 \(\times\) sin(80\textdegree{}) \(\approx\) 2,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (0.550,1.933) {3,2 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.667,2.000) {8,7 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (1.425,2.351) {?};
\end{tikzpicture}\end{center}


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

cos(\(\widehat{WGL}\)) = \(\dfrac{WG}{GL}\)
\par\addvspace{.5em}
 d'où cos(\(\widehat{WGL}\)) = \(\dfrac{3{,}2}{8{,}7}\)
\par\addvspace{.5em}
On a donc \(\widehat{WGL}\) =ArcCos(\(\dfrac{3{,}2}{8{,}7}\)) \(\approx\)68\textdegree{}\end{document}
