On the BC side of the rectangle ABCD, in which AB = 33, A = 77 point E is marked, so that the angle EAB = 45. Find ED.

If the angle EAB = 45, then the angle AEB = 45 according to the theorem on the sum of the angles of a triangle, in this case ABE. The angles at the base are equal, therefore ABE is isosceles and BE = AB = 33. Hence EC = BC-BE = AD-BE = 77-33 = 44.
CD = AB = 33. Triangle ECD-rectangular, respectively, applying the Pythagorean theorem, we find ED = square root of (EC ^ 2 + CD ^ 2) = square root (44 ^ 2 + 33 ^ 2) = 55.