Answer:
Since ∠CAB = 90°, we know that AC is the hypotenuse of the right triangle ABC. Let's use the sine function to find the length of AC:
sin(∠ABC) = BC/AB
sin(46°) = BC/9.4
BC = 9.4 * sin(46°)
Now, using the Pythagorean theorem, we can find the length of AC:
AC = sqrt(AB^2 + BC^2)
AC = sqrt(9.4^2 + (9.4*sin(46°))^2)
AC ≈ 12.632
Rounding this to 3 significant figures, we get:
AC ≈ 12.6
Therefore, the length of AC rounded to 3 significant figures is approximately 12.6 units.