The law of cosines is used to find the value of m.

sin(28) = m/27
            or
m = 27 x (sin(28))

That's the easy way to find it, but if they want you to use cos, that is really tricky. They give you everything that cos would show.

you could just show      a^2 + b^2 = c^2

(18)^2 + b^2 = (27)^2
324 + b^2 = 729
b^2 = 405
b = square root of 405
b = 20.1246117975