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.

\(\frac{21}{h} = \frac{15}{9}\)

\(h = \frac{21(9)}{15}\)

\( h = 12.6\)

\(\frac{21}{i} = \frac{15}{10}\)

\(i = \frac{21(10)}{15}\)

\(i = 14\)