Let `k` be the length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is called a regular tetrahedron). Show that the angel between any edge and a face not containing the edge is`cos^(-1)(1//sqrt(3))` .

Explanation

To show that the angle between any edge and a face not containing the edge in a regular tetrahedron is \( \cos^{-1} \left( \frac{1}{\sqrt{3}} \right) \), we can follow these steps:

### Step 1: Understand the Geometry of the Tetrahedron
A regular tetrahedron has four vertices, which we can label as \( O, A, B, \) and \( C \). Each edge of the tetrahedron has the same length \( k \).

### Step 2: Identify the Edge and the Face
We will consider the edge \( OA \) and the face \( OBC \). Our goal is to find the angle between the edge \( OA \) and the plane formed by the triangle \( OBC \).

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