Solution: First, compute the area of the triangle using Heron's formula. The semi-perimeter $ s = \frac10 + 13 + 152 = 19 $ km. The area $ A = \sqrt19(19-10)(19-13)(19-15) = \sqrt19 \cdot 9 \cdot 6 \cdot 4 = \sqrt4104 = 64.07 $ km² (approximate). The shortest altitude corresponds to the longest side (15 km). Using $ A = \frac12 \cdot \textbase \cdot \textheight $, the altitude $ h = \frac2A15 = \frac2 \cdot 64.0715 \approx 8.54 $ km. For exact value, simplify $ \sqrt4104 = \sqrt4 \cdot 1026 = 2\sqrt1026 $, but numerical approximation suffices here. Thus, the shortest altitude is $ \boxed8.54 $ km. - Veritas Home Health