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 BC:
sin(∠ABC) = BC/AC
sin(64°) = BC/9.1
BC = 9.1 * sin(64°)
Now, using the Pythagorean theorem, we can find the length of AB:
AB = sqrt(AC^2 - BC^2)
AB = sqrt(9.1^2 - (9.1*sin(64°))^2)
AB ≈ 5.222
Rounding this to 3 significant figures, we get:
AB ≈ 5.22
Therefore, the length of AB rounded to 3 significant figures is approximately 5.22 units.