So if you are good at math (I'm decent) then I'd like some help. I have a theoretical triangle, but the problem is: it is a right triangle, and all three sides are the same length, two of which are given for the sides forming the right angle. The longest side is equal to the other sides. I would like to know if it is solvable. Here's a picture for reference:

It is really annoying me and I MUST find the answer. And yes, this is the image I found the problem from...

If it was on a sphere, it would work...

In a right triangle a^2 + b^2 = c^2

If a == b == c then a == b == c == 0

Assuming that diagram is correct then x = sqrt(722) == 26.870057685088805927232085759984263493

Is there more to this problem that would help indicate the "trick"? Otherwise your description contradicts the rest of the information provided.

The other option is non-euclidean geometry (possibly spherical, hyperbolic, etc).

No, this is not solvable. If it is a right triangle, the sides cannot all be the same length, assuming we aren't talking about triangles on the surface of a sphere.

I'm not so great at non-euclidean geometry but I think for this triangle to be on the surface of a sphere, the sphere would need a radius of 38 / Pi.

Thanks guys for the responses, I found this and I guess my description of the problem didn't help as much as I had thought. I had saved the picture a while ago and I tried and tried but couldn't find a solution.. Thanks I'll try what bmenrigh said, using non-euclidean geometry.. If a solution is found I'd like to know about it!

Well if the triangle is on the surface of a sphere see:

http://www.smith.edu/physics/felder/cur ... angle.html
and
https://en.wikipedia.org/wiki/Elliptic_geometry

If you assume you have a 19x19x19 triangle taking up 1/8th the surface area of a sphere then the sphere has a radius of 38 / Pi.

Yes, it must be 1/8th of the surface of a sphere of circumference 4*19 = 76, so that all 3 sides have a length of 19, and all 3 angles are 90 degrees. Simple.

Just think about the curved triangular surface of a "corner" piece on a 2x2x2 puzzle ball.

EDIT. The triangle could also be on an ellipsoid or other curved surface, but that would be a lot more tricky to define and figure out. So there are actually multiple solutions to this problem, which means that the question itself is actually not solvable because it doesn't provide enough information on the shape of the surface, and the person who wrote this question is not as clever as he/she thinks.