In a right triangle XYZ, the sum of the measures of angle y and angle z is equal to 90 degrees, so angle z = 90 - y.
We can use the given information to find the values of sin(z), cos(z), and tan(z):
sin(z) = sin(90 - y) = cos(y) = 0.906
cos(z) = cos(90 - y) = sin(y) = 0.423
tan(z) = tan(90 - y) = cot(y) = 1/tan(y) = 1/0.466 = 2.144
Now we can use the Pythagorean theorem to find the length of the hypotenuse:
sin^2(y) + cos^2(y) = 1
0.423^2 + cos^2(y) = 1
cos^2(y) = 1 - 0.423^2
cos(y) = sqrt(1 - 0.423^2) = 0.906
Finally, we can use the definition of cosine to find cos(x):
cos(x) = adj/hyp
cos(x) = cos(y)/hyp
cos(x) = 0.906/hyp
We do not have enough information to find the value of hypotenuse, so we cannot determine the value of cos(x).