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\begin{document}

\sloppy

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

 Dans le triangle ZBL rectangle en Z, on sait que :
\begin{itemize}
\item ZL=7,8 cm
\item \(\widehat{BLZ}\) =  32\textdegree{}
\end{itemize}

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

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

 Dans le triangle PDJ rectangle en P, on sait que :
\begin{itemize}
\item PD=1,2 cm
\item PJ=4 cm
\end{itemize}

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

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

 Dans le triangle VFK rectangle en V, on sait que :
\begin{itemize}
\item VF=9,4 cm
\item \(\widehat{VFK}\) = 67\textdegree{}
\end{itemize}

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

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

 Dans le triangle VRN rectangle en V, on sait que :
\begin{itemize}
\item VR=9 cm
\item \(\widehat{VRN}\) = 73\textdegree{}
\end{itemize}

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

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

 Dans le triangle WFT rectangle en W, on sait que :
\begin{itemize}
\item WF=1,9 cm
\item WT=5,1 cm
\end{itemize}

Après avoir fait un schéma, calcule l'arrondi au degré près de la mesure de l'angle \(\widehat{WFT}\). \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 (5.100,0.717) {32°};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{ZLB}\)) = \(\dfrac{ZB}{ZL}\)
\par\addvspace{.5em}
d'où  tan(32\textdegree{}) =  \(\dfrac{ZB}{7{,}8}\)
\par\addvspace{.5em}
On a donc ZB =  7,8 \(\times\) tan(32\textdegree{})  \(\approx\) 4,9 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 2}

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

\par\addvspace{.5em}
tan(\(\widehat{PJD}\)) = \(\dfrac{PD}{PJ}\)
\par\addvspace{.5em}
d'où  tan(\(\widehat{PJD}\)) =  \(\dfrac{1{,}2}{4}\)
\par\addvspace{.5em}
 On a donc \(\widehat{PJD}\) =  ArcTan(\(\dfrac{1{,}2}{4}\)) \(\approx\) 17\textdegree{}
\needspace{4\baselineskip}
\subsection*{
Exercice 3}

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\end{tikzpicture}\end{center}


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

cos(\(\widehat{VFK}\)) = \(\dfrac{VF}{FK}\)
\par\addvspace{.5em}
 d'où cos(67\textdegree{}) = \(\dfrac{9{,}4}{FK}\)
\par\addvspace{.5em}
On a donc FK = \(\dfrac{9{,}4}{\cos(67^{\circ})}\)\(\approx\) 24,1 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 4}

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

\par\addvspace{.5em}
tan(\(\widehat{VRN}\)) = \(\dfrac{VN}{VR}\)
\par\addvspace{.5em}
d'où tan(73\textdegree{}) =\(\dfrac{VN}{9}\)
\par\addvspace{.5em}
On a donc VN = 9 \(\times\) tan(73\textdegree{}) \(\approx\) 29,4 cm
\needspace{4\baselineskip}
\subsection*{
Exercice 5}

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  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (6.050,0.954) {T};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (0.550,1.933) {1,9 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (3.500,0.754) {5,1 cm};
  \node[black, anchor=base, font=\fontsize{22.8}{27.3}\selectfont] at (1.430,2.299) {?};
\end{tikzpicture}\end{center}


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

\par\addvspace{.5em}
tan(\(\widehat{WFT}\)) = \(\dfrac{WT}{WF}\)
\par\addvspace{.5em}
d'où tan(\(\widehat{WFT}\)) = \(\dfrac{5{,}1}{1{,}9}\)
\par\addvspace{.5em}
 On a donc WFT = ArcTan(\(\dfrac{5{,}1}{1{,}9}\)) \(\approx\) 70\textdegree{}\end{document}
