Return of the Higs

Remember when I decided to make a post about the Higs Boson, realised I had no idea what it was really and then posted it anyway? Well I decided to be a little bit less lazy when I read this article and thought I should at least know a tiny bit more than this journalist!

Found this video by sixty symbols plus a lovely article from the institute of physics. I still don't really understand why this particle has to exist. I mean I thought you were allowed to assume that mass was just a property of certain particles. A property of me is that I have brown eyes, although of course that is due to my genes so is the Higs particle like a gene? Anyway, back to what I do know! The Higs particle creates a field and this field is what makes particles experience a mass but the field is even harder to detect so they are looking for the particle instead. But the particle decays super fast and they can't detect it so they are trying to find the things that it decays into such as z bosons and photons of certain frequencies. I'm slightly happier though of course can't be content till I really understand!

Frustrated! Help please?

So today I sat an exam for one of my maths modules and I think it went well except for one question. One question that nobody I have spoken to could do and even now with google at hand I still cannot do! I assumed there must be some kind of theorem for this but if there is I can't find it. I usually laugh at people who use the student room after an exam because it doesn't help anyone - the exam is over. But I decided that the frustration of not knowing the answer was bigger than the frustration of knowing I could have known the answer this time! But I still can't find the answer!?

I know nobody reads this but it would be amazing if anybody could find the answer? I'm just about to email my teacher so you can race her!

So the radius of the sector was 6cm and the angle was in radians. We had to find the radius of the circle. I tried everything I can think of including drawing out a rough sketch of a complete circle with this pattern repeated 6 times, trying to use congruent triangles and drawing in a new diameter from the centre of the sector downwards... Is it to do with tangents? Or a theorem? Help?