Given a cube with edge a. Find: the angle between the diagonal and the plane of the base value a = 1.

Let us construct a diagonal BD at the base of the cube and, according to the Pythagorean theorem, in a right-angled triangle ABC determine its length.

BD ^ 2 = AD ^ 2 + AB ^ 2 = 1 ^ 2 + 1 ^ 2 = 2.

ВD = √2 cm.

Let’s construct a diagonal BD1.

The angle between the base plane and the diagonal BD1 is the linear angle DBD1.

In a right-angled triangle BDD1, tgDBD1 = DD1 / BD = 1/1 * √2 = √2 / 2.

Angle DBD1 = arctan (√2 / 2) ≈ 350.

Answer: The angle between the diagonal and the base plane is 350.