Spoiler for My 2 cents

I think the probability of triangle being obtuse is near 1 for an infinite plane

Choose any 2 points shown with the blue line below;

Now, as long as the third point is within the two red lines, the triangle is acute otherwise obtuse

Choose any 2 points shown with the blue line below;

Now, as long as the third point is within the two red lines, the triangle is acute otherwise obtuse

For an infinte plance, the probability of third point within these two lines is near zero.

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