Frequently, in problems involving forces and their components, you have to deal with more than one force at the same time. Here is an example: a weight is being supported with two strings that meet at a knot, with T1 = tension force in the left-side string and T2 = tension force in the right-side string.
You are supposed to draw right triangles to represent the horizontal (x) and vertical (y) components of the two forces. Most students try to draw the triangles directly onto the existing diagram like this:
There are two things wrong with this. For one thing, the diagram becomes very cluttered and hard to use (I have added color, but a student working with just a pencil wouldn't be able to do that). For another, there is a tendency to see the two vertical force components as being equal to each other:
because the force component triangles are drawn side-by-side, with the vertical components given the same "length". If you look carefully at the original sketch above, you will notice that the left-side string is more vertical than the right-side string, which means that it provides more of an upward force (the two upward components could only be equal if the two strings made the same angles with a vertical line).
To avoid these problems entirely, you should construct separate diagrams. You should also make the triangles nice and big to make room for all the labels, and to make the trig functions easier to figure out.
Now we have no reason to assume that the vertical sides are equal. In fact, we don't have to use the same "scale" in both diagrams.