Step-by-step explanation:

Given that ∠ZA = 30°, ∠ZB = 90°, and BC = 20 cm in triangle ABC.

We can use trigonometric ratios in a right-angled triangle:

1. **Using the sine ratio:**

\(\sin(\angle ZA) = \frac{BC}{AB}\)

\(\sin(30°) = \frac{20}{AB}\)

Solving for AB:

\(AB = \frac{20}{\sin(30°)}\)

2. **Using the cosine ratio:**

\(\cos(\angle ZA) = \frac{AB}{BC}\)

\(\cos(30°) = \frac{AB}{20}\)

Solving for AB:

\(AB = 20 \cdot \cos(30°)\)

The value of \(\cos(30°)\) is \(\frac{\sqrt{3}}{2}\).

Therefore, AB = \(20 \cdot \frac{\sqrt{3}}{2} = 10 \sqrt{3}\) cm.

So, the correct answer is B. \(40, 20 \sqrt{3}\).