Final answer:
Given the information mlx = 51°, x = 5, and y = 2, and applying the Law of Sines, it's determined that no triangle can be formed because the requirements cannot be satisfied with these measurements. Therefore, the answer is zero distinct triangles.
Step-by-step explanation:
To determine how many distinct triangles can be formed given the conditions mlx = 51°, x = 5, and y = 2, we must apply the Law of Sines, which relates the lengths of sides of a triangle to the sines of its opposite angles. According to the Law of Sines, for a triangle with sides a, b, and c opposite angles A, B, and C respectively, the ratio a/sin(A) = b/sin(B) = c/sin(C) must hold true.
Since one angle is given as 51°, we can denote this angle as angle A. The side x=5 can be thought of as side a, and the side y=2 as side b. The question to ask is if the given side lengths can form a triangle, which depends on whether there exists an angle B such that the ratio x/sin(mlx) is equal to y/sin(B). If such an angle exists and is less than 180° - A, then a triangle is possible.
However, in our case, since x is significantly larger than y (5 compared to 2), and given that sin(51°) is less than 1, there is no angle B that would satisfy the Law of Sines since sin(B) would have to be greater than 1, which is impossible. Therefore, no triangle can be formed, and the answer is zero distinct triangles.