Since it's a right angle, you can do the Pythagorean theorem backwards. Let's call the 9mm side A, the missing side B, and the longest side C.
[tex] a^{2} + b^{2} = c^{2}
[/tex]
[tex] 9^{2} + b^{2} = 15^{2} [/tex]
[tex] 81 + b^{2} = 225 [/tex]
[tex] b^{2} = 225 - 81[/tex]
[tex] b^{2} = 144[/tex]
[tex] b = 12[/tex]
The answer is 12mm