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\begin{document}

\sloppy

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

 Dans le triangle SVP rectangle en S, on sait que :
\begin{itemize}
\item SP=3,8 cm
\item VP=7,3 cm
\end{itemize}

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

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

 Dans le triangle RSW rectangle en R, on sait que :
\begin{itemize}
\item SW=0,4 cm
\item \(\widehat{RSW}\) = 58\textdegree{}
\end{itemize}

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

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

 Dans le triangle KLZ rectangle en K, on sait que :
\begin{itemize}
\item LZ=8,3 cm
\item \(\widehat{LZK}\) =  34\textdegree{}
\end{itemize}

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

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

 Dans le triangle PWT rectangle en P, on sait que :
\begin{itemize}
\item PT=6,2 cm
\item WT=7,4 cm
\end{itemize}

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

 Dans le triangle RVB rectangle en R, on sait que :
\begin{itemize}
\item RB=4,5 cm
\item \(\widehat{VBR}\) =  43\textdegree{}
\end{itemize}

Après avoir fait un schéma, calcule la longueur du segment [BV]. (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 (3.772,0.860) {?};
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 Dans le triangle SVP rectangle en S, on cherche une relation entre l'angle aigu   \(\widehat{SPV}\) son coté adjacent et l'hypoténuse du triangle.

cos(\(\widehat{SPV}\)) = \(\dfrac{SP}{VP}\)
\par\addvspace{.5em}
  d'où    cos(\(\widehat{SPV}\)) =  \(\dfrac{3{,}8}{7{,}3}\)
\par\addvspace{.5em}
On a donc \(\widehat{SPV}\) = Arccos (\(\dfrac{3{,}8}{7{,}3}\)) \(\approx\) 59\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

cos(\(\widehat{RSW}\)) = \(\dfrac{RS}{SW}\)
\par\addvspace{.5em}
d'où cos(58\textdegree{}) = \(\dfrac{RS}{0{,}4}\)

On a donc RS = 0,4 \(\times\) cos(58\textdegree{}) \(\approx\) 0,2 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

cos(\(\widehat{KZL}\)) = \(\dfrac{KZ}{LZ}\)
\par\addvspace{.5em}
  d'où    cos(34\textdegree{}) =  \(\dfrac{KZ}{8{,}3}\)

On a donc KZ = 8,3 \(\times\) cos(34\textdegree{}) \(\approx\) 6{,}9 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
sin(\(\widehat{PWT}\)) =  \(\dfrac{PT}{WT}\)
\par\addvspace{.5em}
 d'où sin(\(\widehat{PWT}\)) = \(\dfrac{6{,}2}{7{,}4}\)
\par\addvspace{.5em}
On a donc \(\widehat{PWT}\) =  ArcSin(\(\dfrac{6{,}2}{7{,}4}\)) \(\approx\) 57\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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\end{tikzpicture}\end{center}


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

cos(\(\widehat{RBV}\)) = \(\dfrac{RB}{VB}\)
\par\addvspace{.5em}
  d'où    cos(43\textdegree{}) =  \(\dfrac{4{,}5}{VB}\)
\par\addvspace{.5em}
 On a donc VB =  \(\dfrac{4{,}5}{\cos(43^{\circ})}\) \(\approx\) 6,2 cm\end{document}
