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Answers
If 5.8 m is the horizontal side, then vertical side cannot exceed .7 * 5.8 = 4.06 m.
If 5.8 m is the vertical side, then the horizontal must be at least 5.8 / .7 = 8.286 m.
Once you pick a horizontal side and a vertical side then the hypotenuse, by the Pythagorean theorem will be √(x^2+y^2) where x,y are the horizontal and vertical sides.
One sample such triangle: 5.8 m, 3.9 m, 6.99 m.
There are infinitely many triangles satisfying the conditions of the problem.
Obviously, that's not enough information to determine the hypotenuse. I could draw any number of triangles that fit those restrictions. Are you sure that you don't have ANY more information? Such as, is the the 5.8 m side horizontal, or vertical?
You throw it in a dark room and demand answers. If it gives you the wrong answer, you put that belt to good use.