The resultant of two forces can be found using the formula for the magnitude of the sum of two vectors. In this case, the two forces are represented by vectors in the east and north-east directions.

The force acting towards the east can be represented as a vector (A = 5\hat{i}), where (\hat{i}) is a unit vector in the east direction.

The force acting towards the north-east can be represented as a vector (B = 4(\hat{i} + \hat{j})/\sqrt{2}), where (\hat{j}) is a unit vector in the north direction. The division by (\sqrt{2}) is because the vector is at a 45° angle to both the east and north directions.

The resultant force (R = A + B = 5\hat{i} + 4(\hat{i} + \hat{j})/\sqrt{2} = (5 + 4/\sqrt{2})\hat{i} + 4\hat{j}/\sqrt{2}).

The magnitude of this resultant force is given by (\sqrt{(5 + 4/\sqrt{2})^2 + (4/\sqrt{2})^2} = \sqrt{41 + 20\sqrt{2}}) units.