https://file.aiquickdraw.com/mathbot/file/1727336888814hs8f88lh.jpg

The given image shows a right triangle \( XYZ \) with:

- \( XY = 15 \) (adjacent to angle \( X \)),
- \( YZ = 8 \) (opposite to angle \( X \)),
- \( XZ = 17 \) (hypotenuse).

You are asked to find \( \cos X \).

### Cosine formula:
\[
\cos X = \frac{\text{Adjacent}}{\text{Hypotenuse}}
\]

From the triangle:
- The side adjacent to \( X \) is \( XY = 15 \),
- The hypotenuse is \( XZ = 17 \).

Thus:
\[
\cos X = \frac{15}{17}
\]

So the correct answer is **Option C**.

Would you like more details or explanations? Here are some related questions:

1. How do you calculate sine and tangent for this triangle?
2. What are some typical uses of trigonometric ratios in real-life scenarios?
3. How can the Pythagorean theorem verify the sides of this triangle?
4. What are the other trigonometric identities involving cosine?
5. How does the cosine function behave in different quadrants?

**Tip:** Always identify which sides correspond to "opposite," "adjacent," and "hypotenuse" before applying trigonometric ratios.

Find the value of cos X in a right triangle where the sides are XY = 15 (adjacent), YZ = 8 (opposite), and XZ = 17 (hypotenuse).

This problem demonstrates how to find the cosine of angle X in a right triangle, where the sides are XY = 15, YZ = 8, and XZ = 17. The solution applies the cosine formula (Adjacent/Hypotenuse) to solve for cos(X).

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