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The problem is asking to determine the value of \( x \) based on a cosine rule expression. 

From the image, option C is selected, and the expression is:

\[
x = \sqrt{2.50^2 + 2.00^2 - 2(2.50)(2.00)\cos(100.0^\circ)}
\]

This is a classic cosine law formula, used to find the third side of a triangle when two sides and the included angle are given:

\[
c^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]

Now, let's compute the value of \( x \).The value of \( x \) is approximately 3.46 (rounded to two decimal places).

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

1. What is the cosine rule, and when is it typically used in geometry?
2. How would the result change if the angle was less than 90 degrees?
3. Can you apply the sine rule to this problem instead of the cosine rule?
4. What happens to the cosine law when the angle is exactly 90 degrees?
5. How do we determine which side corresponds to \( x \) when using the cosine rule?

**Tip**: Always ensure that the angle is in the correct unit (radians or degrees) when using trigonometric functions on a calculator.

Determine the expression that can be evaluated to find x, and calculate its value based on the cosine rule.

Learn how to calculate the length of a side in a triangle using the cosine rule. In this example, two sides and the included angle are given. The cosine rule formula is applied to find the third side. The result for x is approximately 3.46.

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