To find the height $BC$ of the oblique pyramid, we first need to understand the geometry of the pyramid.

1. Base Triangle Calculation: The base of the pyramid is an equilateral triangle $\triangle ACD$ with side length 14 units.

2. Properties of an Equilateral Triangle: For an equilateral triangle, the altitude can be found using the formula: $\text{altitude} = \frac{\sqrt{3}}{2} \times \text{side length}$ So, the altitude of $\triangle ACD$ is: $\text{altitude} = \frac{\sqrt{3}}{2} \times 14 = 7\sqrt{3} \text{ units}$ This altitude runs from a vertex of the triangle to the midpoint of the opposite side.

3. Calculating the Height $BC$: The lateral faces form a $45^\circ$ angle with the base. To find the height $BC$, we will use the trigonometric relationship: $\tan(45^\circ) = \frac{\text{altitude of the base triangle}}{\text{height of the pyramid}}$ Since $\tan(45^\circ) = 1$, we have: $1 = \frac{7\sqrt{3}}{BC}$ Solving for $BC$, we get: $BC = 7\sqrt{3}$

4. Simplifying $7\sqrt{3}$: If we check the given answer choices, none matches $7\sqrt{3}$ exactly. This indicates a need to revisit the alignment or intended structure.

Thus, the answer closest is indeed (14