The problem involves solving a right triangle $\triangle ABC$, where angle $C = 90^\circ$, side $a = 19.2$ cm, and the hypotenuse $c = 45.6$ cm. We are required to find side $b$, using the Pythagorean theorem.

The Pythagorean theorem states: $a^2 + b^2 = c^2$

We can rearrange this equation to solve for $b$: $b^2 = c^2 - a^2$ $b = \sqrt{c^2 - a^2}$

Now, let's substitute the given values: $b = \sqrt{45.6^2 - 19.2^2}$

I will now calculate the value of $b$.The length of side $b$ is approximately $41.36$ cm when rounded to the nearest hundredth.

Would you like more details on the steps or have any questions? Here are some related questions you might find helpful:

1. How do you solve for unknown angles in a right triangle?
2. What other methods can you use to solve right triangles?
3. How does the Pythagorean theorem apply in real-world problems?
4. Can you find the angles $A$ and $B$ using trigonometric ratios?
5. How do trigonometric functions like sine and cosine relate to the sides of a right triangle?

Tip: When solving right triangles, knowing two sides lets you calculate the third side using the Pythagorean theorem, and then you can find the angles using trigonometric ratios.