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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°.

Find x. Round your answer to the nearest tenth of a degree.

Learn how to solve for angle x in a right triangle using the inverse tangent function. This problem involves trigonometric ratios and is suitable for students in Grades 9-11. The solution includes step-by-step calculations and rounding the answer to the nearest tenth of a degree.

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