please help. Law of Sines & The Law of Cosines assignment.

Question

Determine the number of possible triangles with the given information.

 b = 8, c = 9, and β = 35º.

a) two

b) none

c) one

Answer 1

I am assuming β is opposite side b.

law of cosine, 8²=a²+9²-2*a*9*cos(35)

solving for a in quadradic

a=(18*cos(35)/2)+/-(√((18*cos(35))²-68))/2 , a=1.25 or a=13.50

since "a" can take on two postiive values, there are two triangles possible