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\newcommand{\titre}{Trigonométrie}
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\begin{document}

\sloppy

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

 Dans le triangle FAN rectangle en F, on sait que :
\begin{itemize}
\item FN=4,1 cm
\item AN=7,2 cm
\end{itemize}

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

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

 Dans le triangle MLB rectangle en M, on sait que :
\begin{itemize}
\item LB=8 cm
\item \(\widehat{MLB}\) = 69\textdegree{}
\end{itemize}

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

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

 Dans le triangle CGK rectangle en C, on sait que :
\begin{itemize}
\item CK=9,3 cm
\item \(\widehat{CGK}\) = 70\textdegree{}
\end{itemize}

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

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

 Dans le triangle VWP rectangle en V, on sait que :
\begin{itemize}
\item VW=2,8 cm
\item WP=7 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{VWP}\).
\needspace{4\baselineskip}
\section*{
Exercice 5}

 Dans le triangle ZCJ rectangle en Z, on sait que :
\begin{itemize}
\item ZC=5,8 cm
\item \(\widehat{CJZ}\) =  18\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [JC]. (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 (3.667,2.000) {7,2 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.879,0.843) {?};
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 Dans le triangle FAN rectangle en F, on cherche une relation entre l'angle aigu   \(\widehat{FNA}\) son coté adjacent et l'hypoténuse du triangle.

cos(\(\widehat{FNA}\)) = \(\dfrac{FN}{AN}\)
\par\addvspace{.5em}
  d'où    cos(\(\widehat{FNA}\)) =  \(\dfrac{4{,}1}{7{,}2}\)
\par\addvspace{.5em}
On a donc \(\widehat{FNA}\) = Arccos (\(\dfrac{4{,}1}{7{,}2}\)) \(\approx\) 55\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{MLB}\)) =  \(\dfrac{MB}{LB}\)
\par\addvspace{.5em}
 d'où sin(69\textdegree{}) = \(\dfrac{MB}{8}\)

On a donc MB = 8 \(\times\) sin(69\textdegree{}) \(\approx\) 7,5 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
tan(\(\widehat{CGK}\)) = \(\dfrac{CK}{CG}\)
\par\addvspace{.5em}
tan(70\textdegree{}) = \(\dfrac{9{,}3}{CG}\)
\par\addvspace{.5em}
 On a donc CG = \(\dfrac{9{,}3}{\tan(70^{\circ})}\) \(\approx\) 3,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

cos(\(\widehat{VWP}\)) = \(\dfrac{VW}{WP}\)
\par\addvspace{.5em}
 d'où cos(\(\widehat{VWP}\)) = \(\dfrac{2{,}8}{7}\)
\par\addvspace{.5em}
On a donc \(\widehat{VWP}\) =ArcCos(\(\dfrac{2{,}8}{7}\)) \(\approx\)66\textdegree{}
\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) {5,8 cm};
  \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 (5.292,1.242) {18°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{ZJC}\)) = \(\dfrac{ZC}{CJ}\)
\par\addvspace{.5em}
 D'où sin(18\textdegree{}) = \(\dfrac{5{,}8}{CJ}\)
\par\addvspace{.5em}
On a donc CJ =\(\dfrac{5{,}8}{\sin(18^{\circ})}\) \(\approx\) 18,8 cm\end{document}
