Can you find the lengths of the 2 sides of a triangle if you know the length of the hypotenuse but none of the angles?

Answer 1

No. With only the length of the hypotenuse (which is the side opposite the right angle in a right triangle), and no other information, you cannot find the length of the other sides. Want to see it? Draw an x-y axis, and then draw a segment from the origin out and up to the right (in the first quadrant) a short distance. Nothing fancy. Now drop a perpendicular from the end of the segment you just drew down to the x axis. There's your right triangle with your "known" hypotenuse. Now just move the hypotenuse "up" or "down" a bit and draw your "new" perpendicular to the x axis. Same hypotenuse, different triangle. And you can draw an infinite number of these. Yes, there will be a relationship between the 2 sides you're looking for. The sum of their squares will equal the square of the hypotenuse, but other than that, you can't say more.