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\begin{document}

\sloppy

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

 Dans le triangle RAB rectangle en R, on sait que :
\begin{itemize}
\item RB=1 cm
\item \(\widehat{ABR}\) =  45\textdegree{}
\end{itemize}

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

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

 Dans le triangle HWV rectangle en H, on sait que :
\begin{itemize}
\item HV=4,4 cm
\item WV=9,3 cm
\end{itemize}

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

 Dans le triangle HML rectangle en H, on sait que :
\begin{itemize}
\item HL=2 cm
\item \(\widehat{MLH}\) =  22\textdegree{}
\end{itemize}

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

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

 Dans le triangle PRZ rectangle en P, on sait que :
\begin{itemize}
\item PR=2,5 cm
\item \(\widehat{PRZ}\) = 80\textdegree{}
\end{itemize}

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

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

 Dans le triangle RHA rectangle en R, on sait que :
\begin{itemize}
\item RH=3 cm
\item HA=8,9 cm
\end{itemize}

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

\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 (4.284,0.788) {45°};
\end{tikzpicture}\end{center}


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

cos(\(\widehat{RBA}\)) = \(\dfrac{RB}{AB}\)
\par\addvspace{.5em}
  d'où    cos(45\textdegree{}) =  \(\dfrac{1}{AB}\)
\par\addvspace{.5em}
 On a donc AB =  \(\dfrac{1}{\cos(45^{\circ})}\) \(\approx\) 1,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
sin(\(\widehat{HWV}\)) =  \(\dfrac{HV}{WV}\)
\par\addvspace{.5em}
 d'où sin(\(\widehat{HWV}\)) = \(\dfrac{4{,}4}{9{,}3}\)
\par\addvspace{.5em}
On a donc \(\widehat{HWV}\) =  ArcSin(\(\dfrac{4{,}4}{9{,}3}\)) \(\approx\) 28\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

\par\addvspace{.5em}
tan(\(\widehat{HLM}\)) = \(\dfrac{HM}{HL}\)
\par\addvspace{.5em}
d'où  tan(22\textdegree{}) =  \(\dfrac{HM}{2}\)
\par\addvspace{.5em}
On a donc HM =  2 \(\times\) tan(22\textdegree{})  \(\approx\) 0,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{PRZ}\)) = \(\dfrac{PZ}{PR}\)
\par\addvspace{.5em}
d'où tan(80\textdegree{}) =\(\dfrac{PZ}{2{,}5}\)
\par\addvspace{.5em}
On a donc PZ = 2,5 \(\times\) tan(80\textdegree{}) \(\approx\) 14,2 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (5.293,1.170) {?};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
sin(\(\widehat{RAH}\)) = \(\dfrac{RH}{HA}\)
\par\addvspace{.5em}
d'où sin(\(\widehat{RAH}\)) =\(\dfrac{3}{8{,}9}\)
\par\addvspace{.5em}
 On a donc \(\widehat{RAH}\) = ArcSin(\(\dfrac{3}{8{,}9}\)) \(\approx\) 20\textdegree{}\end{document}
