Calculating the Size of an Atom

Background to Question:

We can measure the size of atoms in a crystal by x-ray diffraction. A number of elements crystallize into cubic structures, typically face-centred or body-centred cubic.

Strontium is an example of an element which crystallizes on the face centred lattice and barium is an example of an element which crystallizes on the body centred lattice. the cubic lattice parameters for these elements (the dimension a on the figure) are 6.08 and 5.02 Å respectively (1 Å = 10^-10m).

Question:

Assume the strontium and barium atoms to be hard spheres and furthermore that they touch along the face diagoal in the case of the face centred cubic, and along the body diagonal in the case of the body centred cubic. Using what you have learned in the trigonometry modules calculate the atomic diameters of strontium and barium.