If I was to try and undertake this project, I would look into/befamilliar with 3 things:
-Canvas (I mean BASIC canvas, use a framework, even)
-KnockoutJS (for declarative binding and dom manipulation)
Here's how I would go about it:
1. Get your webpage up and running (or use some IDE that will let you test)
2. Make a relatively small canvas element, and draw a triangle in it (so you'd have to set up the draw loop for the triangle I guess)
3. Find out and familiarize yourself with how to get at the vertices and actual points of the triangle
4. Use knockoutJS (make them observables, and print them somewhere on the page below the canvas as spans
5. Add math, make computed observables that do the calculations you need (sin/cos/etc)
6. At this point, you want to focus now, on making those vertices draggable (from here, you'll see just how easy/hard it is to make a dynamic one -- I suspect it won't be too hard with a good framework that redraws for you, worst comes to worst you could just redraw lines after detecting movement by dragging on the vertices)
7. At this point, all you need to work on is making it prettier -- look into CSS3 for neat overlay and positioning tricks
It's super doable, maybe even easy (since the math is simple and the concept is relatively simple)