A regular tetrahedron is a 3D figure that has four congruent triangular faces.

You can make a regular tetrahedron (like the one pictured) by printing the tetrahedron net found at

http://www.mathsisfun.com/geometry/tetrahedron-model.html

Note: you may have to reduce the size of your print to get the net to fit on one page. 90% works well for me.

The atoms in a molecule of methane ${\mathrm{CH}}_4$are arranged in a tetrahedral pattern where the carbon atom is at the center of the tetrahedron and each hydrogen atom occupies a corner of the tetrahedron.

Use the following figure to calculate the angle between any two hydrogen atoms relative to the center of the carbon atom.

The side length of the cube is 1. Thus $\overline{\mathrm{PT}}=1$

Use the Pythagorean formula to compute the length of $\overline{\mathrm{QP}}$. Thus $\overline{\mathrm{QP}}=\sqrt{1^2+1^2}=\sqrt{2}$

R is a point exactly halfway between points Q and P. Thus $\overline{\mathrm{RP}}=\frac{\sqrt{2}}{2}$ and $\overline{\mathrm{RO}}=\frac{1}{2}$

The tangent of angle$\angle \mathrm{ROP}$ is the ratio of sides $\overline{\mathrm{RP}}$and $\overline{\mathrm{RO}}$. Thus $\arctan \left(\frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}}\right)=\arctan \sqrt{2}=54.73561032°$

Since hydrogen atoms occupy the locations at points Q and P, the angle $\angle \mathrm{QOP}=2\times \angle \mathrm{ROP}=109.5°$