strange disappointment

Early in the semester we were assigned a reading in which a former T440 student retold a story of having someone "spoil" the answer to an inquiry she was undertaking. She was furious. At the time I read that I thought it was a bit silly. What's the big deal? There are plenty of other things to occupy your thoughts.
This week in class we did the mirror fieldwork. I really cannot remember ever having so much fun exploring physics (or whatever we were doing.) I had no idea what the answer was, and was delighted that each time we made a new discovery we would realize there was another variable involved in the question ("but, what if the people aren't the same distance from the mirror?"). When we were at the stage of asking ourselves how one could measure the angles without a measuring device or trial and error, someone in our group said something about angle of incident and something else being equal. She started drawing some graphs and I tried to ignore it but she was insistent. I started getting really angry. I don't want to see your graphs! We are so close to figuring this out on our own! I had to physically disconnect. She and another in our group continued with the graph drawing, while I tried to convince the other group member that we could us our arms to gauge the angles in the absence of string. Eventually, the graph drawers realized that they were no closer to an idea of how to determine where to put the mirror without measuring, so I felt vindicated.