This problem involves a right triangle $ABC$ with angle $C = 90^\circ$. You are given the lengths of sides $a = 44.7$ inches and $b = 35.8$ inches, where $a$ and $b$ represent the two legs of the right triangle. The goal is to find the measure of angle $B$.

We can use the following trigonometric relation for right triangles:

$\tan(B) = \frac{a}{b}$

Now, solving for $B$:

$B = \tan^{-1}\left( \frac{a}{b} \right)$

Let me calculate that.The measure of angle $B$ is approximately $51.3^\circ$.

Would you like any further details or have any additional questions?

Here are 5 related questions to explore:

1. How can you calculate angle $A$ in this right triangle?
2. What is the hypotenuse of the triangle given sides $a$ and $b$?
3. How would you solve for angle $B$ if different side lengths were given?
4. Can you apply the Law of Cosines to this triangle even though it is a right triangle?
5. What would change if angle $B$ were given instead of the side lengths?

Tip: Always double-check trigonometric ratios by ensuring you're using the right function for the given information (e.g., $\sin$, $\cos$, $\tan$).