I still don't understand.

It is difficult to know how answer this since you didn't answer my question.
I was not trying to trip you up, just find out what you have been taught/know about vectors and their addition.
No you don't discard the information in the triangles. As Woody says they give you the directions of the individual vectors.
The way I suggested is the way a draughtsman would solve this  by drawing to scale.
He would draw the 5,3 and 5,12 right angled triangles (What do you know about right angles triangles and these numbers?)and extend their hypotenuses to scale to represent the first two vectors.
Then he would actually draw the polygon parallel to these, head to tail, just as I said.
Finally he could then measure the magnitude and direction of the resultant.
An alternative would be to use the triangles to calculate the horizontal and vertical components of each vector.
The add up the horizontal and vertical components separately to form horizontal and vertical resultants.
Then combine the H and V resultants in a vecotr triangle to form the overall resultant.
Then calculate the length and direction of this overall resultant from the vector triangle.
Perhaps you were taught this latter method?