Solution: First, calculate the area of the triangle using Heron's formula. The semi-perimeter $ s = \frac13 + 14 + 152 = 21 $. The area is $ \sqrt21(21-13)(21-14)(21-15) = \sqrt21 \cdot 8 \cdot 7 \cdot 6 = \sqrt7056 = 84 \, \textkm^2 $. The altitudes correspond to each side: $ h_a = \frac2 \times 8413 \approx 12.92 $, $ h_b = \frac2 \times 8414 = 12 $, $ h_c = \frac2 \times 8415 = 11.2 $. The shortest altitude is $ \boxed11.2 $ km. - Appfinity Technologies