Using similar triangles, we see that 12/x = x/16. Multiplying by 16x, we see that x^2=12*16=192.
By the Pythagorean Theorem, \(12^2+y^2=x^2\). Since x^2=192, we know that \(144+y^2=192\). Subtracting 144 from both sides, we see that \(y^2=48\), so y=\(4 \sqrt{3}\).
