Let's call the length of the side opposite angle K "x". If the hypotenuse is 1.75 times longer than this side, then the length of the hypotenuse can be expressed as 1.75x.
In a right triangle, the relationship between the lengths of the sides and the angles can be expressed using the Pythagorean theorem:
x^2 + y^2 = c^2, where c is the length of the hypotenuse.
Since the length of the hypotenuse is 1.75x, we can substitute this value for c in the equation:
x^2 + y^2 = (1.75x)^2
Expanding the right side of the equation:
x^2 + y^2 = 3.0625x^2
Subtracting x^2 from both sides:
0 = 2.0625x^2
Dividing both sides by 2.0625:
0 = x^2
Since x represents the length of a side of the triangle, it cannot be negative. Therefore, x must be equal to 0.
If x = 0, then y = 0 as well, and the triangle degenerates into a single point with no angles.
Since x cannot equal 0, there is no solution to this problem and the measure of angle K cannot be found