A = 27.5°, a = 15.0 cm, b = 36.4 cm

According to the law of sines, a/sin(A) = b/sin(B), plugging in the values:

15/sin(27.5) = 36.4/sin(B) One can rearrange this to be

sin(B) = (36.4/15) sin(27.5) = 1.12

Of course this is not possible because the sine function cannot be greater than 1.

So there is no triangle with the values of length and angle given.

It is not possible to solve.