1. \( a=4, \beta=27^{\circ} ; b, c \)

It seems like you're providing some values for a triangle, specifically \( a = 4 \) and \( \beta = 27^\circ \). However, to find the other sides \( b \) and \( c \), we need more information. Typically, in a triangle, if you have one side and the angle opposite to it, you can use the Law of Sines or the Law of Cosines to find the other sides or angles. If you have another angle or side, please provide that information. If not, we can only express \( b \) and \( c \) in terms of the unknown angle \( \alpha \) or \( \gamma \) (the other two angles in the triangle). Please provide additional details or clarify your question!