The Primary Trig Ratios should be the very first concept everyone should see if they could use to solve on a triangle. SOH CAH TOA ratios only works to solve the missing values for a right triangle. The primary trig ratio works for the picture below because it is a right triangle and theres an angle and a side we could use to solve the triangle.
Sine Law can be used if the triangle is not a right triangle and there are two sides with the corresponding angle. The sine law works for triangles that can be labeled like the picture below. The sine law can be used with any triangle if given the right sides and angles.
The cosine law should be used when sine law and the primary trig ratios do not work. The cosine would only be used if theres an angle and there are two other angles that do not correspond with the sides. Cosine works with the diagram below because the opposite side of the angle is unknown.
If all of the methods can be used in a situation I would choose the Primary Trig Ratios because i believe it is the fastest and easiest method. I have been using the primary trig ratios since grade 10 so it would make sense to keep using it.
In grade 10, I only knew about the primary trig ratios. The method limits my abilities to solve all triangles because it only works on right triangles. Now I know multiple ways to solve a triangle. I did not realize how indept trigonometry can go into. I can also predict if the ratios would be positive or negative using the Cast Rule.