Rectangle ABCD and square ABMN lie in mutually perpendicular planes.

Rectangle ABCD and square ABMN lie in mutually perpendicular planes. Find the angle between straight line MD and plane ABC, if AB = a, BC = a √2.

By condition, the ABMN plane is perpendicular to the ABCD plane. Let’s draw the diagonal BD of the rectangle.

Since the segment BD belongs to the plane ABCD, and the segment BM belongs to the plane ABMН, then BM is perpendicular to BD, and the triangle BMD is rectangular.

From the right-angled triangle ABD, by the Pythagorean theorem, we determine the length of the hypotenuse BD.

BD ^ 2 = AB ^ 2 + AD ^ 2 = a ^ 2 + (a√2) ^ 2 = 3 * a ^ 2.

BD = a * √3 cm.

In a right-angled triangle BDM tgBDM = BM / BD = a / a * √3 = 1 / √3 = √3 / 3.

Arctg (√3 / 3) = 30.

Answer: The angle between straight line MD and plane ABCD is 30.