$$ABC$$ is a triangle in the XY plane, whose vertices are $$A (0, 0, 0)$$, $$B (5, 0, 0)$$, and $$C (3, 4, 0)$$. A point $$D (x, y, z)$$ lies above the XY plane (i.e. $$z > 0$$ ), such that $$AD = 5$$, $$BD = 6$$, and $$CD = 7$$. Find the value of z.