Double Flee A

The circle and the triangle, done up here by bigdubb (don't miss the full vector-based hotness diagram), wouldn't let me sleep. I couldn't figure it out on my own, so, a beaten man, I took to the geometry websites like surface tension takes to golden-gate bridge jumpers.

In case you missed it, the problem: for a circle with radius 4, with an equilateral triangle in it touching the circle with its points, what is the area of the triangle. Solve from scratch.

I failed to solve it from scratch, but I had different people sending me different answers, so I owed it to them to figure it out any which way I could. Turns out there's a handy little equation for triangles where the side, angle, and side are knowns, that we had all forgotten about.

area = 1/2 times a times b times sin c, where sides a and b are connected by angle with c degrees.

The triangle comes out to 20.785, which fills 41.35 per cent of the circle's area.

In a curious twist of fate, the bum who was talking nonsense (see this for details, at the end), and who I almost forgot to mention at all, was actually closer than two-thirds of the people who responded to this when he said (for no reason?) "twenty-two-seven." The world is a strange place.

posted by dale @ 2:04 AM