In a regular rectangular pyramid SABCD with equal edges, find the angle between the diagonal AC of the base and the side edge SC.

Since the length of all edges of the pyramid is the same, we denote it by X cm.

Let us define the edge length AC by the Pythagorean theorem.

AC ^ 2 = AD ^ 2 + SD ^ 2 = X ^ 2 + X ^ 2 = 2 * X ^ 2.

AC = X * √2 cm.

Since the diagonals of the square at the base of the pyramid are divided in half, then OS = OA = AC / 2 = X * √2 / 2.

The SОС triangle is rectangular, then CosSCO = OC / SC = (X * √2 / 2) / X = √2 / 2.

Angle SCO = arcos (√2 / 2) = 45.

Answer: The angle between the diagonal AC of the base and the side edge SC is 45.