Why is the tetrahedral bond angle 109°? The tetrahedron-in-a-cube

The common question of why the tetrahedral angle is 109.471° can be answered using a tetrahedron-in-a-cube, along with some Year 10 level mathematics. The tetrahedron-in-a-cube can also be used to demonstrate the non-polarity of tetrahedral molecules, the relationship between different types of lattice structures, and to demonstrate that inductive reasoning does not always provide the correct answer.