Question

In triangle ABC, you know that a = 2, b = 3 and m < A = 30°. Which option below lists the number of triangles and gives the correct explanation?
There are no triangles because b sin A < a.
There is exactly one triangle because b sin A = 0.5b.
There are two triangles because b sin A < a < b.
There are three triangles because b sin A = 0.5b and b sin A < a < b.

Answer 1

Apply the Law of Sines.
sinB/b = sinA/a
sinB/3 = sin(30°)/2
sinB = (3/2)sin(30°) = 0.75

Therefore
bsinA = 3*sin(30) = 1.5
0.5b = 0.5*3 = 1.5

Answer:
There is exactly one triangle because b sinA  = 0.5b.

Answer 2

That person who answered wrong