Here's one possibility; I used t for the optional argument for the minipages (to get top vertical alignment) and baseline=(current bounding box.north) for the tikzpicture. I also removed a spurious blank space after the first \end{minipage} so that now the width for both minipages can add up to \linewidth. Also I used font=\scriptsize for the nodes of the diagram. Depending on the desired position for the label "Problem " one can obtain different alternatives; the following code shows two possibilities:
\documentclass[a4paper, 12pt]{article}
\usepackage{fouriernc}
\usepackage{amsmath,amsfonts,enumerate,tabularx,calrsfs,esvect, multicol}
\usepackage{graphics}
\usepackage[left=15mm,right=20mm,top=15mm,bottom=10mm]{geometry}
\usepackage[thmmarks,standard,thref]{ntheorem}
\usepackage{pgf,tikz,lipsum}
\usetikzlibrary{arrows}
\pagestyle{empty}
\theoremseparator{.}
\theorembodyfont{\upshape}
%\theorembodyfont{\normalfont}
\newtheorem{pro}{Problem}
\renewcommand{\baselinestretch}{1.5}
\begin{document}
\thispagestyle{empty}
\lipsum[2]
\begin{pro}
Solve the following equations:
\begin{enumerate}[\quad 1)]
\item $\dfrac{\cos^2 2x}{\cos x + \cos\dfrac{\pi}{4}} = \cos x - \cos\dfrac{\pi}{4}$;
\item $\dfrac{\cos^2 2x}{\cos x + \cos\dfrac{\pi}{4}} = \cos x - \cos\dfrac{\pi}{4}$;
\item $(\sqrt{3}\sin x + 2\cos x)\cdot (1 - \cos x) = \sin^2 x$.
\end{enumerate}
\end{pro}
\begin{pro}\mbox{}\\
\begin{minipage}[t]{0.3\linewidth}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm,baseline=(current bounding box.north),every node/.append style={font=\scriptsize}]
\clip(-0.5,-0.5) rectangle (4.3,4.5);
\draw (0,0)-- (4,0);
\draw (4,0)-- (2,3.46);
\draw (2,3.46)-- (0,0);
\fill [color=black] (0,0) circle (1.5pt);
\draw[color=black] (-0.03,-0.19) node {$B$};
\fill [color=black] (4,0) circle (1.5pt);
\draw[color=black] (4.1,-0.19) node {$C$};
\fill [color=black] (2,3.46) circle (1.5pt);
\draw[color=black] (1.99,3.72) node {$A$};
\end{tikzpicture}
\end{minipage}%
\begin{minipage}[t]{0.7\linewidth}
Write the equation of the plane which passes the point and perpendicular to the line $\Delta$
\end{minipage}
\end{pro}
\noindent\begin{minipage}[t]{0.3\linewidth}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm,baseline=(current bounding box.north),every node/.append style={font=\scriptsize}]
\clip(-0.5,-0.5) rectangle (4.3,4.5);
\draw (0,0)-- (4,0);
\draw (4,0)-- (2,3.46);
\draw (2,3.46)-- (0,0);
\fill [color=black] (0,0) circle (1.5pt);
\draw[color=black] (-0.03,-0.19) node {$B$};
\fill [color=black] (4,0) circle (1.5pt);
\draw[color=black] (4.1,-0.19) node {$C$};
\fill [color=black] (2,3.46) circle (1.5pt);
\draw[color=black] (1.99,3.72) node {$A$};
\end{tikzpicture}
\end{minipage}%
\begin{minipage}[t]{0.7\linewidth}
\begin{pro}
Write the equation of the plane which passes the point and perpendicular to the line $\Delta$
\end{pro}
\end{minipage}
\end{document}

As a personal note, perhaps you could reconsider the change for \baselinestretch?
Another request has been made in a comment: the problem to the left, the figure to the right:
\documentclass[a4paper, 12pt]{article}
\usepackage{fouriernc}
\usepackage{amsmath,amsfonts,enumerate,tabularx,calrsfs,esvect, multicol}
\usepackage{graphics}
\usepackage[left=15mm,right=20mm,top=15mm,bottom=10mm]{geometry}
\usepackage[thmmarks,standard,thref]{ntheorem}
\usepackage{pgf,tikz,lipsum}
\usetikzlibrary{arrows}
\pagestyle{empty}
\theoremseparator{.}
\theorembodyfont{\upshape}
%\theorembodyfont{\normalfont}
\newtheorem{pro}{Problem}
\renewcommand{\baselinestretch}{1.5}
\begin{document}
\thispagestyle{empty}
\noindent\begin{minipage}[t]{0.7\linewidth}
\begin{pro}
Write the equation of the plane which passes the point and perpendicular to the line $\Delta$
\end{pro}
\end{minipage}%
\begin{minipage}[t]{0.3\linewidth}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm,baseline=(current bounding box.north),every node/.append style={font=\scriptsize}]
\clip(-0.5,-0.5) rectangle (4.3,4.5);
\draw (0,0)-- (4,0);
\draw (4,0)-- (2,3.46);
\draw (2,3.46)-- (0,0);
\fill [color=black] (0,0) circle (1.5pt);
\draw[color=black] (-0.03,-0.19) node {$B$};
\fill [color=black] (4,0) circle (1.5pt);
\draw[color=black] (4.1,-0.19) node {$C$};
\fill [color=black] (2,3.46) circle (1.5pt);
\draw[color=black] (1.99,3.72) node {$A$};
\end{tikzpicture}
\end{minipage}
\end{document}
