### Instruction: A regular tetrahedron is a triangular pyramid in which each face is an equilateral triangle.  If the height of a regular tetrahedron is 20 inches then what is the length of each edge of the tetrahedron? Express your answer in simplest radical form.### Response: To solve this problem, I need to relate the height of the tetrahedron to the length of its edges.
I know that the height of a regular tetrahedron is given by the formula h = sqrt(2/3) * a, where a is the length of an edge.
This formula can be derived by considering a right triangle formed by the height, the center of a face, and a vertex of the tetrahedron.
I can use this formula to find a in terms of h by isolating a.
Multiplying both sides by sqrt(3/2), I get a = sqrt(3/2) * h.
Plugging in h = 20, I get a = sqrt(3/2) * 20.
Simplifying, I get a = 10 * sqrt(6).
Therefore, the length of each edge of the tetrahedron is 10 * sqrt(6) inches.