+269 In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.
+129771 Semi-perimeter = [ 15 + 9 + 10 ] / 2 = 17
Area = sqrt [ 17 * 2 * 7 * 8 ] = 4 sqrt 119
Shortest altitude is drawn to the longest side
4 sart 119 = (1/2) AB * Altityude
4 sqrt 119 = (1/2) 15 * Altitude
[ 4 sqrt 119 ] / [ 1/2 * 15 ] = [8 sqrt 119] / 15 = Altitude ≈ 5.82
