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\begin{document}

\sloppy

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

 Dans le triangle HWG rectangle en H, on sait que :
\begin{itemize}
\item WG=5,2 cm
\item \(\widehat{HWG}\) = 46\textdegree{}
\end{itemize}

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

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

 Dans le triangle AVB rectangle en A, on sait que :
\begin{itemize}
\item AV=4,5 cm
\item \(\widehat{VBA}\) =  35\textdegree{}
\end{itemize}

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

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

 Dans le triangle JFK rectangle en J, on sait que :
\begin{itemize}
\item JF=1,5 cm
\item FK=9,9 cm
\end{itemize}

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

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

 Dans le triangle KWN rectangle en K, on sait que :
\begin{itemize}
\item KW=2,7 cm
\item KN=4,5 cm
\end{itemize}

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

 Dans le triangle RLV rectangle en R, on sait que :
\begin{itemize}
\item RV=3,5 cm
\item \(\widehat{RLV}\) = 48\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [VL]. (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 (2.311,2.720) {46°};
\end{tikzpicture}\end{center}


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

cos(\(\widehat{HWG}\)) = \(\dfrac{HW}{WG}\)
\par\addvspace{.5em}
d'où cos(46\textdegree{}) = \(\dfrac{HW}{5{,}2}\)

On a donc HW = 5,2 \(\times\) cos(46\textdegree{}) \(\approx\) 3,6 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
tan(\(\widehat{ABV}\)) = \(\dfrac{AV}{AB}\)
\par\addvspace{.5em}
d'où  tan(35\textdegree{}) =  \(\dfrac{4{,}5}{AB}\)
\par\addvspace{.5em}
On a donc AB = \(\dfrac{4{,}5}{\tan(35^{\circ})}\) \(\approx\) 6,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
sin(\(\widehat{JKF}\)) = \(\dfrac{JF}{FK}\)
\par\addvspace{.5em}
d'où sin(\(\widehat{JKF}\)) =\(\dfrac{1{,}5}{9{,}9}\)
\par\addvspace{.5em}
 On a donc \(\widehat{JKF}\) = ArcSin(\(\dfrac{1{,}5}{9{,}9}\)) \(\approx\) 9\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{KWN}\)) = \(\dfrac{KN}{KW}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{KWN}\)) = \(\dfrac{4{,}5}{2{,}7}\)
\par\addvspace{.5em}
 On a donc KWN = ArcTan(\(\dfrac{4{,}5}{2{,}7}\)) \(\approx\) 59\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (2.216,2.724) {48°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{RLV}\)) =  \(\dfrac{RV}{LV}\)
\par\addvspace{.5em}
 d'où sin(48\textdegree{}) = \(\dfrac{3{,}5}{LV}\)
\par\addvspace{.5em}
 On a donc LV = \(\dfrac{3{,}5}{\sin(48^{\circ})}\) \(\approx\) 4,7 cm\end{document}
