This is a right triangle $\triangle ABC$ with the right angle at $B$, the hypotenuse $AC$, and two given side lengths: $AB = 7 \, \text{cm}$ and $BC = 4 \, \text{cm}$. The goal appears to be finding the value of $x^\circ$, the angle at $A$.

To solve for $x$, we can use trigonometric ratios. Specifically, we use the tangent function, as we know the opposite and adjacent sides relative to $x$:

$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{BC}{AB}.$

Calculation:

1. Substitute the known values: $\tan(x) = \frac{4}{7}.$

2. Use the inverse tangent function to find $x$: $x = \tan^{-1}\left(\frac{4}{7}\right).$

3. Calculate $x$: Using a calculator, $x \approx \tan^{-1}(0.5714) \approx 29.74^\circ.$

Final Answer:

$x \approx 29.74^\circ.$

Would you like a detailed explanation of the trigonometric process or assistance with other aspects of the problem?

Related Questions:

1. What is the length of the hypotenuse $AC$ in $\triangle ABC$?
2. How do you calculate the other angle in $\triangle ABC$?
3. How does the Pythagorean theorem verify this triangle?
4. What are some practical uses of trigonometry in solving triangle problems?
5. Can you find the sine and cosine of $x^\circ$ in this triangle?

Tip: Always double-check calculations when using a calculator for inverse trigonometric functions, as rounding errors can occur.