No trig needed, this is linear algebra. The two lines have the form y = m_Ax + b_A and y = m_Bx + b_B. The point where both are satisfied is the intersection you want.

Solving for x, we get x = (b_B - b_A)/(m_A - m_B). Similarly, y = (m_Bb_A - m_Ab_B) / (m_B - m_A).

That is with the numeric values

1. m_A = (D_y - A) / D_x
2. m_B = (C_y - B) / C_x
3. b_A = A
4. b_B = B

I hope I haven't made a mess of this :) It will simplify things a bit that D_x and C_x are equal.