Does the angle-side relationship in triangles correspond with specific triangles or does it apply in all triangles?

Not sure what you mean by "angle-side relationship" in triangles.

The angles and sides are related by the Sine Law and the Cosine Law in trig

If you are looking for something else, have some fun with this:

http://www.mathopenref.com/trianglesideangle.html

The angle-side relationship, commonly known as the side-angle-side (SAS) and angle-side-angle (ASA) conditions, apply to all triangles. These relationships are fundamental properties of triangles and are used to determine whether two triangles are congruent (meaning they have the same shape and size).

To understand the angle-side relationship, let's start with the SAS condition. According to this condition, if two sides of one triangle are congruent to two sides of another triangle, and the included angle (the angle between the two sides) of one triangle is congruent to the included angle of the other triangle, then the two triangles are congruent. This means that all corresponding angles and sides of the triangles will be equal in length.

The ASA condition is similar. It states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

To answer whether these conditions apply only to specific triangles or all triangles, they actually apply to all triangles. As long as the corresponding sides and angles of two triangles satisfy the SAS or ASA conditions, the triangles are guaranteed to be congruent.

So, when you come across a question asking about the angle-side relationship in triangles, you can use the SAS or ASA conditions to determine congruency. Just make sure that you have enough information about the angles and sides of the triangles to apply these conditions.