# Alternative way to calculate the area of a right angled triangle

## Main Question or Discussion Point

Hello all!

New to the forums, and I have a question for you. In my classes, we have been dealing a lot with proofs lately, so when I was working on an assignment, I figured I would try and find my own proof for something, just for the hell of it. I decided to tacle the area of a right angled triangle, because I was using it in one of my assignments, and I wanted to skip some of the legwork I had to do to find the area. On my third try of finding a proof, I finally arrived at something useful.

Starting with Area=½ab, I ended up with:
Area=¼ $c^{2}$sin(2A)=¼ $c^{2}$cos(2B)​

I verified my findings by comparing the results with the ½ab version, and they match. I also wanted to doube check it with some trusted source (and that I wasn't just getting lucky), so I searched around on the web, but can't find it listed anywhere.

So now the question: Has anyone seen this before? And where?

## Answers and Replies

tiny-tim
Homework Helper
welcome to pf!

hello kenneth! welcome to pf!

(actually, it's ¼ $c^{2}$sin(2A)=¼ $c^{2}$sin(2B) )

i don't think it has a name, since it's not particularly useful

but if you double the triangle, by adding a reflection to itself, making a triangle with angles 2A B and B, then it's the well-known formula for the area of a triangle, 1/2 side*side*sin(anglebetween) = 1/2 c*c*sin2A

AlephZero