The remaining side is 15 inches.
We can find this by using the Pythagorean Theorem which is listed below, with a and b being the lengths of the legs of the triangle and c being the lengths of the hypotenuse.
[tex] a^{2} + b^{2} = c^{2} [/tex]
Now we can put the known values in and solve for the remaining leg.
[tex] a^{2} + b^{2} = c^{2} [/tex]
[tex] 36^{2} + b^{2} = 39^{2} [/tex]
[tex] 1296 + b^{2} = 1521 [/tex]
[tex] b^{2} [/tex] = 225
b = 15
