Let \(A\) be the first ship and \(B\) be the second ship.

Velocity, \(V = \frac{distance}{time}\)

After \(2\) hours ship \(A\) travelled \(d_a = 8.5(2) = 17 ~ mi\) while ship \(B\) travelled \(d_b = 10 (2) = 20 ~mi\)

The distance between the ships after 2 hours, can be calculated by \(cos\) law

\(d^2 = d_{b}^2 + d_{a}^2 - 2d_ad_b \cos 45\)

\(d^2 = 20^2 + 17^2 - 2(20)(17) \cos 45\)

\(d^2 = 208.17\)

\(d = 14.43 ~mi\)