Solution:
Since the triangles are similar the ratio and proportion between their corresponding sides is possible.
Let \(h \text{-shortest}\) and \(i\) be the lengths of the remaining side of the triangle.
\(\frac{21}{h} = \frac{15}{9}\)
\(h = \frac{21(9)}{15}\)
\( h = 12.6\)
\(\frac{21}{i} = \frac{15}{10}\)
\(i = \frac{21(10)}{15}\)
\(i = 14\)
Thus, the length of the sides of the triangle are 14, 12.6 and 21 inches.