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\begin{document}

\sloppy

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

 Dans le triangle LTB rectangle en L, on sait que :
\begin{itemize}
\item TB=1,5 cm
\item \(\widehat{TBL}\) =  34\textdegree{}
\end{itemize}

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

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

 Dans le triangle RPL rectangle en R, on sait que :
\begin{itemize}
\item PL=6,4 cm
\item \(\widehat{PLR}\) =  33\textdegree{}
\end{itemize}

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

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

 Dans le triangle GFS rectangle en G, on sait que :
\begin{itemize}
\item GS=1,4 cm
\item \(\widehat{FSG}\) =  23\textdegree{}
\end{itemize}

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

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

 Dans le triangle SKN rectangle en S, on sait que :
\begin{itemize}
\item SK=3 cm
\item SN=4,2 cm
\end{itemize}

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

 Dans le triangle SJV rectangle en S, on sait que :
\begin{itemize}
\item SJ=1,7 cm
\item JV=8,5 cm
\end{itemize}

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

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

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

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

\par\addvspace{.5em}
sin(\(\widehat{LBT}\)) = \(\dfrac{LT}{TB}\)
\par\addvspace{.5em}
 D'où sin(34\textdegree{}) = \(\dfrac{LT}{1{,}5}\)

On a donc LT = 1,5 \(\times\) sin(34\textdegree{}) \(\approx\) 0,8 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

cos(\(\widehat{RLP}\)) = \(\dfrac{RL}{PL}\)
\par\addvspace{.5em}
  d'où    cos(33\textdegree{}) =  \(\dfrac{RL}{6{,}4}\)

On a donc RL = 6,4 \(\times\) cos(33\textdegree{}) \(\approx\) 5{,}4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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

cos(\(\widehat{GSF}\)) = \(\dfrac{GS}{FS}\)
\par\addvspace{.5em}
  d'où    cos(23\textdegree{}) =  \(\dfrac{1{,}4}{FS}\)
\par\addvspace{.5em}
 On a donc FS =  \(\dfrac{1{,}4}{\cos(23^{\circ})}\) \(\approx\) 1,5 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{SKN}\)) = \(\dfrac{SN}{SK}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{SKN}\)) = \(\dfrac{4{,}2}{3}\)
\par\addvspace{.5em}
 On a donc SKN = ArcTan(\(\dfrac{4{,}2}{3}\)) \(\approx\) 54\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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

\par\addvspace{.5em}
sin(\(\widehat{SVJ}\)) = \(\dfrac{SJ}{JV}\)
\par\addvspace{.5em}
d'où sin(\(\widehat{SVJ}\)) =\(\dfrac{1{,}7}{8{,}5}\)
\par\addvspace{.5em}
 On a donc \(\widehat{SVJ}\) = ArcSin(\(\dfrac{1{,}7}{8{,}5}\)) \(\approx\) 12\textdegree{}\end{document}
