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\begin{document}

\sloppy

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

 Dans le triangle TRH rectangle en T, on sait que :
\begin{itemize}
\item TR=2,2 cm
\item RH=7,2 cm
\end{itemize}

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

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

 Dans le triangle RLD rectangle en R, on sait que :
\begin{itemize}
\item RL=2,4 cm
\item RD=5,3 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{RLD}\).
\needspace{4\baselineskip}
\section*{
Exercice 3}

 Dans le triangle JPR rectangle en J, on sait que :
\begin{itemize}
\item PR=2 cm
\item \(\widehat{PRJ}\) =  27\textdegree{}
\end{itemize}

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

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

 Dans le triangle VHC rectangle en V, on sait que :
\begin{itemize}
\item VC=5,2 cm
\item \(\widehat{VHC}\) = 59\textdegree{}
\end{itemize}

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

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

 Dans le triangle ASR rectangle en A, on sait que :
\begin{itemize}
\item AS=3,3 cm
\item \(\widehat{SRA}\) =  44\textdegree{}
\end{itemize}

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

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

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

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 Dans le triangle TRH rectangle en T, on cherche une relation entre l'angle aigu   \(\widehat{THR}\) son coté opposé et l'hypoténuse du triangle.

\par\addvspace{.5em}
sin(\(\widehat{THR}\)) = \(\dfrac{TR}{RH}\)
\par\addvspace{.5em}
d'où sin(\(\widehat{THR}\)) =\(\dfrac{2{,}2}{7{,}2}\)
\par\addvspace{.5em}
 On a donc \(\widehat{THR}\) = ArcSin(\(\dfrac{2{,}2}{7{,}2}\)) \(\approx\) 18\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
tan(\(\widehat{RLD}\)) = \(\dfrac{RD}{RL}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{RLD}\)) = \(\dfrac{5{,}3}{2{,}4}\)
\par\addvspace{.5em}
 On a donc RLD = ArcTan(\(\dfrac{5{,}3}{2{,}4}\)) \(\approx\) 66\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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\end{tikzpicture}\end{center}


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

cos(\(\widehat{JRP}\)) = \(\dfrac{JR}{PR}\)
\par\addvspace{.5em}
  d'où    cos(27\textdegree{}) =  \(\dfrac{JR}{2}\)

On a donc JR = 2 \(\times\) cos(27\textdegree{}) \(\approx\) 1{,}8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{VHC}\)) = \(\dfrac{VC}{VH}\)
\par\addvspace{.5em}
tan(59\textdegree{}) = \(\dfrac{5{,}2}{VH}\)
\par\addvspace{.5em}
 On a donc VH = \(\dfrac{5{,}2}{\tan(59^{\circ})}\) \(\approx\) 3,1 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (4.332,0.783) {44°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{ARS}\)) = \(\dfrac{AS}{SR}\)
\par\addvspace{.5em}
 D'où sin(44\textdegree{}) = \(\dfrac{3{,}3}{SR}\)
\par\addvspace{.5em}
On a donc SR =\(\dfrac{3{,}3}{\sin(44^{\circ})}\) \(\approx\) 4,8 cm\end{document}
