In a regular rectangular pyramid SABCD with equal edges, find the angle between the diagonal AC of the base and the side edge SC.
February 14, 2021 | education
| 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.
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