To determine which trigonometric ratio to use to find \( x \), you need to consider the relationship between the angle, the adjacent side, the opposite side, and the hypotenuse in the context of a right triangle. Here’s a brief overview of when to use each trigonometric ratio:
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Sin (sine): Used when you have the opposite side and want to find the hypotenuse or the angle. The ratio is \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
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Cos (cosine): Used when you have the adjacent side and want to find the hypotenuse or the angle. The ratio is \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
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Tan (tangent): Used when you have the opposite side and the adjacent side. The ratio is \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).
Without additional context about the triangle or what \( x \) represents (angle, side length, etc.), it is difficult to specify which ratio to use. If you can provide more information such as which sides you have or what \( x \) refers to, I can help you determine the correct trigonometric ratio to use.
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