Project ID:
5000000068
Accepted:
Template:
Question:
\vspace{-2em}
\begin{minipage}{0.55\linewidth}
The base $ABCD$ of a square pyramid $ABCDV$ has an edge of length $a$, and the lateral face is an equilateral triangle (see the picture). Let $S$ be the midpoint of the base $ABCD$ and let $P$ be the midpoint of the edge $AV$. Find the angle between
\end{minipage}
\hfill
\begin{minipage}{0.4\linewidth}
\obrMsr[x=3cm,y=3cm,z=0.3cm]{-1}2{-1}2
{
\footnotesize
\pgfmathsetmacro{\cubex}{1}
\pgfmathsetmacro{\cubey}{1}
\pgfmathsetmacro{\cubez}{2}
\coordinate (A) at (0,0,0);
\coordinate (B) at (\cubex,0,0);
\coordinate (C) at (\cubex.2,0,\cubez);
\coordinate (D) at (0.2,0,\cubez);
\coordinate (V) at (0.6,0.7,1);
\coordinate (P) at ($(A)!0.5!(V)$);
\draw[thick,dashed] (A) -- (D) node [yshift=4pt,xshift=-6pt]{$D$} -- (C) node [yshift=-5pt,xshift=5pt]{$C$};
\draw[dashed] (A) -- (C);
\draw[dashed] (B) -- (D);
\draw (0.6,0,1) node [below,xshift=-2pt,yshift=1pt]{$S$};
\draw[thick] (A) node [yshift=-5pt,xshift=-5pt]{$A$} -- (B) node [yshift=-6pt,xshift=3pt]{$B$} --(C);
\draw[thick] (A) -- (V) node [above]{$V$};
\draw[thick] (B) -- (V);
\draw[thick] (C) -- (V);
\draw[thick,dashed] (D) -- (V);
\draw[dashed] (0.6,0,1) -- (V);
\begin{scope}[thick]
\obrKrizek[2pt]{P}{above left}{P}
\end{scope}
}
\end{minipage}
Answer Header 1:
$30^{\circ}$
Answer Header 2:
$45^{\circ}$
Answer Header 3:
$60^{\circ}$
Answer Header 4:
$90^{\circ}$
Question Row 1:
\ifen the lines $AD$ and $DC$: \fi \ifcs přímkami $AD$ a $DC$: \fi \ifpl prostymi $AD$ i $DC$: \fi \ifsk priamkou $AD$ a $DC$: \fi \ifes las rectas $AD$ y $DC$: \fi
Answer Row 1:
4
Question Row 2:
\ifen the lines $BV$ and $BC$: \fi \ifcs přímkami $BV$ a $BC$: \fi \ifpl prostymi $BV$ i $BC$: \fi \ifsk priamkou $BV$ a $BC$: \fi \ifes las rectas $BV$ y $BC$: \fi
Answer Row 2:
3
Question Row 3:
\ifen the lines $BP$ and $BV$: \fi \ifcs přímkami $BP$ a $BV$: \fi \ifpl prostymi $BP$ i $BV$: \fi \ifsk priamkou $BP$ a $BV$: \fi \ifes las rectas $BP$ y $BV$: \fi
Answer Row 3:
1
Question Row 4:
\ifen the lines $AD$ and $VS$: \fi \ifcs přímkami $AD$ a $VS$: \fi \ifpl prostymi $AD$ i $VS$: \fi \ifsk priamkou $AD$ a $VS$: \fi \ifes las rectas $AD$ y $VS$: \fi
Answer Row 4:
4
Question Row 5:
\ifen the lines $AB$ and $CV$: \fi \ifcs přímkami $AB$ a $CV$: \fi \ifpl prostymi $AB$ i $CV$: \fi \ifsk priamkou $AB$ a $CV$: \fi \ifes las rectas $AB$ y $CV$: \fi
Answer Row 5:
3
Question Row 6:
\ifen the lines $AC$ and $DC$: \fi \ifcs přímkami $AC$ a $DC$: \fi \ifpl prostymi $AC$ i $DC$: \fi \ifsk priamkou $AC$ a $DC$: \fi \ifes las rectas $AC$ y $DC$: \fi
Answer Row 6:
2
Question Row 7:
\ifen the lines $AP$ and $BV$: \fi \ifcs přímkami $AP$ a $BV$: \fi \ifpl prostymi $AP$ i $BV$: \fi \ifsk priamkou $AP$ a $BV$: \fi \ifes las rectas $AP$ y $BV$: \fi
Answer Row 7:
3
Question Row 8:
\ifen the lines $AC$ and $DV$: \fi \ifcs přímkami $AC$ a $DV$: \fi \ifpl prostymi $AC$ i $DV$: \fi \ifsk priamkou $AC$ a $DV$: \fi \ifes las rectas $AC$ y $DV$: \fi
Answer Row 8:
4
Tex:
% tiket 33179
\MsrTabulka[0pt]{0.5\linewidth}{0.45\linewidth}
\pocetsloupcu{4}