## The Tetrahedron

The tetrahedron is a four sided shape. Each side is a equilateral triangle.

We can find angles in the tetrahedron using only the properties of right angled triangles – simple triogonometry and Pythagoras theorem. If the length of each side is 1, the length of the line down the middle of one side from the apex the the middle of an edge is

The lines that bisect any of the sides are all length sqrt 3 over 2 . We can construct the triangle inside the tetrahgedron below.

The angle x can be found using the cosine rule.

degrees.

The anggle between an edge and the base is B in the triangle above.

Using the Cosine Rule again asgives

degrees.

The triangle is isoceles since two lengths are the same. The angle at C is then 54.74 degrees.