Question

Find the number of distinct triangles with the measurements a = 5, b = 2, and angle A = 51 degrees

Answer 1

to figure out exactly how many, we apply the following rules

- if angle A >= 90 and a<= b, there are 0 triangles
- if angle A >= 90 and a > b there is 1 triangle
- if angle A < 90 and a < bsin(A) there are 0 triangles
- if angle A < 90 and a = bsinA there is 1 triangle
- if angle A < 90 and bsinA < a < b there are 2 triangles
- if angle A < 90 and b<= a there is 1 triangle

see which of these cases apply to your triangle

source: https://math.stackexchange.com/questions/1386111/how-do-you-determine-the-number-of-triangles-using-ssa