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To solve for \( x \) in the given triangle, we will use trigonometric functions. Here are the steps:

1. **Identify the sides relative to angle \( x \):**
   - Opposite to \( x \): \( 69 \) (length of \( LK \)).
   - Adjacent to \( x \): \( 92 \) (length of \( MK \)).

2. **Use the tangent function:**
   \[
   \tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{69}{92}.
   \]

3. **Calculate the value of \( \tan(x) \):**
   \[
   \tan(x) = \frac{69}{92} \approx 0.75.
   \]

4. **Find \( x \) by taking the arctangent:**
   \[
   x = \tan^{-1}(0.75).
   \]

Let me compute this.import math

# Calculate x using arctangent
opposite = 69
adjacent = 92

# Calculate tan(x) and then find the angle in degrees
tan_x = opposite / adjacent
x_degrees = math.degrees(math.atan(tan_x))
x_degrees36.8698976458440236.86989764584402successThe angle \( x \) is approximately \( 36.9^\circ \) when rounded to the nearest tenth of a degree.

Would you like further explanation or assistance with related questions? Here are some related problems for exploration:

1. What is the measure of the other non-right angle in the triangle?
2. How do you calculate the hypotenuse using the Pythagorean theorem with the given sides?
3. What trigonometric ratio could be used if the hypotenuse and one leg were known instead?
4. Can you solve for \( x \) using cosine instead of tangent? If so, how?
5. How do you verify the accuracy of your answer using the triangle's angles?

**Tip:** Always remember the acronym SOH-CAH-TOA when working with right triangle trigonometry!

Solve for x. Round to the nearest tenth of a degree, if necessary.

Discover how to solve for the angle x in a right triangle using the tangent function and arctangent calculation. Learn the step-by-step process, including identifying sides and using the tan(x) = opposite/adjacent formula. This problem is ideal for Grades 9-10.

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