To solve for $x$ in the given right triangle, we need to use trigonometric ratios. The given triangle has:

• Opposite side (to angle $x$): 42 units
• Adjacent side (to angle $x$): 22 units

We can use the tangent function, which relates the opposite side to the adjacent side in a right triangle:

$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{42}{22}$

Now, let's solve for $x$ by taking the inverse tangent (arctan) of the ratio:

$x = \tan^{-1}\left(\frac{42}{22}\right)$

I will calculate this value and round it to the nearest tenth of a degree.The value of $x$ is approximately 62.4° when rounded to the nearest tenth of a degree.

Would you like more details or have any questions? Here are some related questions that could deepen your understanding:

1. How would you find the length of the hypotenuse in this triangle?
2. What is the sine of angle $x$ in this triangle?
3. How can you use the cosine function to find angle $x$?
4. How would the angle $x$ change if the opposite side was longer?
5. What if you knew the hypotenuse and one leg—how could you find angle $x$?

Tip: Remember, for right triangles, the sum of the angles always equals 180°, with one angle being 90°.