Answer:
no solution
Explanation:
The Law of Sines tells you the relationship between sides and angles of a triangle.
Law of Sines
The Law of Sines tells you ...
sin(A)/a = sin(B)/b = sin(C)/c
Using the given information, this would tell us ...
sin(55°)/12 = sin(B)/b = sin(C)/27
Then angle C would be ...
sin(C) = (27/12)sin(55°) ≈ 1.843
There is no angle whose sine is greater than 1. The triangle we seek does not exist. (Side BC is too short relative to side AB.)