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\begin{document}

\sloppy

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

 Dans le triangle RJV rectangle en R, on sait que :
\begin{itemize}
\item JV=0,8 cm
\item \(\widehat{JVR}\) =  26\textdegree{}
\end{itemize}

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

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

 Dans le triangle HVA rectangle en H, on sait que :
\begin{itemize}
\item HA=1,1 cm
\item \(\widehat{HVA}\) = 48\textdegree{}
\end{itemize}

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

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

 Dans le triangle JCF rectangle en J, on sait que :
\begin{itemize}
\item JC=2,7 cm
\item JF=5,5 cm
\end{itemize}

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

 Dans le triangle VRF rectangle en V, on sait que :
\begin{itemize}
\item RF=7,6 cm
\item \(\widehat{VRF}\) = 69\textdegree{}
\end{itemize}

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

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

 Dans le triangle ZKT rectangle en Z, on sait que :
\begin{itemize}
\item ZT=5,3 cm
\item KT=8,2 cm
\end{itemize}

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

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

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

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

\par\addvspace{.5em}
sin(\(\widehat{RVJ}\)) = \(\dfrac{RJ}{JV}\)
\par\addvspace{.5em}
 D'où sin(26\textdegree{}) = \(\dfrac{RJ}{0{,}8}\)

On a donc RJ = 0,8 \(\times\) sin(26\textdegree{}) \(\approx\) 0,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{HVA}\)) =  \(\dfrac{HA}{VA}\)
\par\addvspace{.5em}
 d'où sin(48\textdegree{}) = \(\dfrac{1{,}1}{VA}\)
\par\addvspace{.5em}
 On a donc VA = \(\dfrac{1{,}1}{\sin(48^{\circ})}\) \(\approx\) 1,5 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
tan(\(\widehat{JCF}\)) = \(\dfrac{JF}{JC}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{JCF}\)) = \(\dfrac{5{,}5}{2{,}7}\)
\par\addvspace{.5em}
 On a donc JCF = ArcTan(\(\dfrac{5{,}5}{2{,}7}\)) \(\approx\) 64\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
sin(\(\widehat{VRF}\)) =  \(\dfrac{VF}{RF}\)
\par\addvspace{.5em}
 d'où sin(69\textdegree{}) = \(\dfrac{VF}{7{,}6}\)

On a donc VF = 7,6 \(\times\) sin(69\textdegree{}) \(\approx\) 7,1 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (4.081,0.814) {?};
\end{tikzpicture}\end{center}


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

cos(\(\widehat{ZTK}\)) = \(\dfrac{ZT}{KT}\)
\par\addvspace{.5em}
  d'où    cos(\(\widehat{ZTK}\)) =  \(\dfrac{5{,}3}{8{,}2}\)
\par\addvspace{.5em}
On a donc \(\widehat{ZTK}\) = Arccos (\(\dfrac{5{,}3}{8{,}2}\)) \(\approx\) 50\textdegree{} \end{document}
