Altitude to hypotenuse \(c = 10\):
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- h_a = \frac{2A}{6} = \frac{48}{6} = 8 \text{ cm}
- Altitude to leg \(b = 8\):
- h_b = \frac{2A}{8} = \frac{48}{8} = 6 \text{ cm}
- h_c = \frac{2A}{10} = \frac{48}{10} = 4.8 \text{ cm}
- The shortest altitude is the one to the hypotenuse: \(\boxed{4.8}\) cm.
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