NiceTriangle

It was my last year in highschool and we were all working hard for the selecction test that applies to University. There was this teacher, a true mathematics lover, that i had before and he was doing some extra classes. The fact is that he had cancer and was really next to pass away, oddly enough with that precarious health he was doing classes. When I asked about it he said he prefered to be working rather than in bed. Then one day someone found a book this teacher wrote (a simple exercises book) that had this problem as the last one... unsolved. He told us that this was an easy problem about elementary geometry, and some other stuff i dont remember. I totally forgot about this, two months later i applied to University and he died next month. When i came back to find this problem later i was intrigued about my inhability to solve it. I asked some University teachers and the best shot i got was "meh this is easy use trigonometry". For about 2 years i came back from time to time just to get dissapointed about it. Luckily enough i solved it some time ago, RIP Domingo Almendras.

Are you sure?? dont give up man come on! fight!
+ Show Spoiler +