[samtheman]

Is it possible for an equalateral triangle to consist of three 90 angles?

When you draw an equilateral triangle on the surface of a sphere, each angle is greater than 60 degrees. As the sphere gets smaller, the angle-size gets larger. Can it reach 90 degrees, or is that approached as a limit?

I don't know.

[Sabertooth]

Can it reach 90 degrees, or is that approached as a limit?

Yes, it can reach 90 degress at all three angles on a sphere.

Consider drawing two line segments southward from the North Pole, with a 90 degree angle between them, until they reached the Equator. The angles of the intersections of those lines at the Equator would also be 90 degrees, giving you three at 90.

[woollyone]

Yes, an equalateral triangle can have thee angles that are 90 degrees each, but not in two dimensions. In three dimensions, the resulting triangle will represent 1/8 of a perfect sphere.

Can the angles be greater than 90 degrees? Not so certain about that one! In order for that to happen in three dimensions, I belive it couldn't be eualateral. I believe that 90 degrees is the maximum in three dimensions for an equalateral triangle.