The image shows a right triangle $\triangle JIH$, with side lengths $JI = 54$ and $HI = 44$, and an angle $x^\circ$ at $J$. We are asked to find the value of $x^\circ$, which is the angle at vertex $J$.

To solve for $x$, we can use trigonometric ratios, specifically the tangent function because we are given the lengths of the opposite side (44) and the adjacent side (54) relative to $x$.

The tangent of an angle in a right triangle is given by: $\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{HI}{JI}$

Substitute the given values: $\tan(x) = \frac{44}{54}$

Now calculate the ratio: $\tan(x) \approx 0.8148$

To find $x$, we take the inverse tangent (arctangent) of 0.8148: $x = \tan^{-1}(0.8148)$

Using a calculator: $x \approx 39.0^\circ$

Thus, the angle $x$ is approximately $39.0^\circ$, rounded to the nearest tenth.

Would you like more details on this solution or further explanation on any steps?

Here are five related questions to expand on this:

1. How do you find the other angle of the triangle?
2. What is the sine of angle $x$?
3. How do you calculate the hypotenuse using the Pythagorean theorem?
4. How can we verify the angle $x$ using the cosine function?
5. What is the general relationship between trigonometric ratios in right triangles?

Tip: Always double-check your rounding when working with degrees to ensure accuracy, especially when asked to round to the nearest tenth.