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This problem involves a right triangle \( \triangle WVU \) with angle \( \angle U = 50^\circ \), hypotenuse \( WU = 6.1 \), and right angle \( \angle VU = 90^\circ \). We need to solve for \( x \), which represents the length of side \( UV \).

Since we are dealing with a right triangle, we can use trigonometric functions to find \( x \). Given that \( \angle U = 50^\circ \) and the hypotenuse is 6.1, we can use the cosine function because:

\[
\cos(50^\circ) = \frac{\text{adjacent (UV)}}{\text{hypotenuse (WU)}}
\]

Thus:

\[
\cos(50^\circ) = \frac{x}{6.1}
\]

Solving for \( x \):

\[
x = 6.1 \times \cos(50^\circ)
\]

I will calculate this for you.The value of \( x \), the length of side \( UV \), is approximately **3.9** when rounded to the nearest tenth.

Would you like more details on how this was calculated, or do you have any further questions?

Here are 5 related questions to consider:
1. How would you solve for side \( WV \) in this triangle?
2. Can you use the sine function to find another side of the triangle?
3. What are the properties of right triangles that allow you to use trigonometry in this way?
4. How would the result change if the angle was larger, such as \( 60^\circ \)?
5. What is the significance of rounding to the nearest tenth in practical problems?

**Tip:** Always ensure your calculator is set to degrees when working with angle measures given in degrees!

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

This problem involves solving for the side of a right triangle using the cosine function. Given the hypotenuse of 6.1 units and a 50° angle, this step-by-step guide helps calculate the length of the adjacent side, rounded to the nearest tenth.

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