Solving 3 Simulatenous Quadratic Equations

Geometry Level 2

\( ABC \) 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.

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