Calculate a set of Cartesian coordinates to 4 significant figures with respect to the origin for the carbon and hydrogen atoms of a methane molecule as shown in below Figure given that the C-H bond distance is 1.091 A and the H-C-H tetrahedral angle is 109.47°, here focus on Methane Molecular Structure.

For ease of calculation note that H^{1}, H^{2} and H^{3} form an equilateral triangle and lie in a plane parallel to the yz-axis. Thus find the coordinates for H° which gives H^{1} by rotation around the z-axis, and then find H^{2} and H^{3} by +120° and —120° rotation about the x-axis of H^{1.}

**Solution**

In above Figure the coordinates of C^{1} are (0, 0, 0) and the coordinates of H^{4} are (-1.091, 0, 0).

H’ can be found by a clockwise (or negative) rotation of 109.47° about the z-axis of H^{4}.

Related Study: