Step-by-step explanation:
A triangle can be formed for b=3 and B=15° as long as side c is between 3 and 3/sin(15°) ≈ 11.59 inches in length. The limit for side c on the high end is that it is opposite a right angle. The limit for side c on the other end is that it is opposite a linear angle.
For the given length of side c, there are two possible triangles with b=3 and B=15°. (See attached.)
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For the given values of b and c, the largest possible value of B is the angle that puts side c opposite a right angle: B ≤ arcsin(3/7) ≈ 25.3769°