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\begin{document}

\sloppy

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

 Dans le triangle KBG rectangle en K, on sait que :
\begin{itemize}
\item KB=1,2 cm
\item BG=8,9 cm
\end{itemize}

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

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

 Dans le triangle VZK rectangle en V, on sait que :
\begin{itemize}
\item ZK=3,4 cm
\item \(\widehat{ZKV}\) =  13\textdegree{}
\end{itemize}

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

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

 Dans le triangle VRS rectangle en V, on sait que :
\begin{itemize}
\item VR=1,4 cm
\item \(\widehat{VRS}\) = 76\textdegree{}
\end{itemize}

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

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

 Dans le triangle WVJ rectangle en W, on sait que :
\begin{itemize}
\item WJ=4,4 cm
\item VJ=9,5 cm
\end{itemize}

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

 Dans le triangle WLS rectangle en W, on sait que :
\begin{itemize}
\item WL=1,7 cm
\item \(\widehat{LSW}\) =  32\textdegree{}
\end{itemize}

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

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

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

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

\par\addvspace{.5em}
sin(\(\widehat{KGB}\)) = \(\dfrac{KB}{BG}\)
\par\addvspace{.5em}
d'où sin(\(\widehat{KGB}\)) =\(\dfrac{1{,}2}{8{,}9}\)
\par\addvspace{.5em}
 On a donc \(\widehat{KGB}\) = ArcSin(\(\dfrac{1{,}2}{8{,}9}\)) \(\approx\) 8\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{VKZ}\)) = \(\dfrac{VZ}{ZK}\)
\par\addvspace{.5em}
 D'où sin(13\textdegree{}) = \(\dfrac{VZ}{3{,}4}\)

On a donc VZ = 3,4 \(\times\) sin(13\textdegree{}) \(\approx\) 0,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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\end{tikzpicture}\end{center}


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

cos(\(\widehat{VRS}\)) = \(\dfrac{VR}{RS}\)
\par\addvspace{.5em}
 d'où cos(76\textdegree{}) = \(\dfrac{1{,}4}{RS}\)
\par\addvspace{.5em}
On a donc RS = \(\dfrac{1{,}4}{\cos(76^{\circ})}\)\(\approx\) 5,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
sin(\(\widehat{WVJ}\)) =  \(\dfrac{WJ}{VJ}\)
\par\addvspace{.5em}
 d'où sin(\(\widehat{WVJ}\)) = \(\dfrac{4{,}4}{9{,}5}\)
\par\addvspace{.5em}
On a donc \(\widehat{WVJ}\) =  ArcSin(\(\dfrac{4{,}4}{9{,}5}\)) \(\approx\) 28\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.500,0.267) {?};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (5.100,0.717) {32°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{WSL}\)) = \(\dfrac{WL}{WS}\)
\par\addvspace{.5em}
d'où  tan(32\textdegree{}) =  \(\dfrac{1{,}7}{WS}\)
\par\addvspace{.5em}
On a donc WS = \(\dfrac{1{,}7}{\tan(32^{\circ})}\) \(\approx\) 2,7 cm\end{document}
