The objective is to determine a measure of the angle between two carbon-hydrogen bonds.\\
A regular tetrahedron is a polyhedron whose four faces are equilateral triangles.

Electrical interactions lead to modeling the methane molecule $\mathrm{CH}_4$ as follows:
\begin{itemize}
  \item The nuclei of hydrogen atoms occupy the positions of the four vertices of a regular tetrahedron.
  \item The carbon nucleus at the center of the molecule is equidistant from the four hydrogen atoms.
\end{itemize}

\begin{enumerate}
  \item Justify that we can inscribe this tetrahedron in a cube ABCDEFGH by positioning two hydrogen atoms at vertices A and C of the cube and the two other hydrogen atoms at two other vertices of the cube.\\
Represent the molecule in the cube given in the appendix on page 6.\\
In the rest of the exercise, we can work in the coordinate system $(A; \overrightarrow{AB}; \overrightarrow{AD}; \overrightarrow{AE})$.
  \item Prove that the carbon atom is at the center $\Omega$ of the cube.
  \item Determine the approximation to the nearest tenth of a degree of the measure of the angle formed between the carbon-hydrogen bonds, that is, the angle $\widehat{A\Omega C}$.
\end{enumerate}