In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.
Shortest altitude is drawn to the longest side
Area (using Heron's Formula) = sqrt [ 17 * 2 * 7 * 8 ] = sqrt [ 1904]
[ABC ] = (1/2) AB * shortest altitude
sqrt [ 1904 ] = (1/2) * 15 * shortest altitude
sqrt [ 1904 ] / 7.5 = shortest altitude ≈ 5.82
+621 
