How many distinct triangles can be formed for which m∠A = 75°, a = 2, and b = 3?

We are given

m∠A = 75 deg

a = 2

b = 3

Apply the Law of Sines.

sin (B) / b = sin (A) / a

sin (B) / 3 = sin (75) / 2

sin (B) = (3*sin (75)) / 2 = 1.45

The value of the sin function cannot exceed 1.

This means that the triangle cannot exist.

Answer: No distinct triangles