Given ABCD – square, BE perpendicular to ABC, angle EAB = 30 degrees. Find the angle between ED and plane AB

Let us denote the length of the side of the square through X cm, AB = BC = CD = AD = X cm.

Then, according to the Pythagorean theorem, the length of the hypotenuse BD is equal to:

BD ^ 2 = AB ^ 2 + AD ^ 2 = 2 * AB ^ 2 = 2 * X ^ 2.

BD = X * √2 cm.

In a right-angled triangle ABE, we determine the length of the leg BE.

Tg30 = BE / AB = BE / X.

BE = X * tg30 = X / √3 cm.

In a right-angled triangle DBE, we define the tangent of the angle BDE.

tgВDE = BE / DE = (X / √3) / X * √2 = 1 / (√3 * √2) = 1 / √6.

Angle ВDE = arctan (1 / √6).

Answer: Angle ВDE = arctan (1 / √6).