To solve for angle $x^\circ$ in the given right triangle, we can use trigonometric functions. Specifically, since we are given the opposite side $63$ and the adjacent side $60$, we use the tangent function:

$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{63}{60}$

Step 1: Calculate the tangent value.

$\frac{63}{60} = 1.05$

Step 2: Find the angle using the inverse tangent ($\tan^{-1}$).

$x = \tan^{-1}(1.05)$

Using a calculator:

$x \approx 46.13^\circ$

Step 3: Round to the nearest tenth.

$x \approx 46.1^\circ$

It seems none of the answer options in your image exactly matches $46.1^\circ$. Double-checking with the available choices, 43.6 and 43.7 are the closest, but they seem slightly off. This might be due to rounding errors or an alternate calculation method being used in the question.

Would you like to explore further or discuss the options given?

Here are five follow-up questions you could explore:

1. How would the solution change if you used sine or cosine instead of tangent?
2. What is the relationship between the three angles in a right triangle?
3. How do calculators compute inverse trigonometric functions internally?
4. How would the calculation change if the triangle were not a right triangle?
5. Could small measurement inaccuracies in side lengths affect the angle result?

Tip: Always double-check your calculator’s mode (degrees vs. radians) when solving trigonometric problems involving angles.