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The altitudes \( h_a \), \( h_b \), and \( h_c \) corresponding to sides \( a = 13 \), \( b = 14 \), and \( c = 15 \) are calculated as follows:
h_a = \frac{2A}{a} = \frac{2 \times 84}{13} = \frac{168}{13} \approx 12.92
h_b = \frac{2A}{b} = \frac{2 \times 84}{14} = 12

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