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To find \(\cos C\) for the given right triangle \(ABC\), we use the definition of the cosine function in a right triangle:

\[
\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}
\]

For angle \(C\) at vertex \(C\):
- The **adjacent side** is \(AB\), which has a length of 15.
- The **hypotenuse** is \(AC\), which has a length of 17.

Therefore:

\[
\cos C = \frac{AB}{AC} = \frac{15}{17}
\]

So, \(\cos C = \frac{15}{17}\).

Would you like more details or have any questions?

Here are 8 related questions you might find useful:
1. How do you calculate the sine of angle \(C\) in this triangle?
2. How do you find the tangent of angle \(C\) in this triangle?
3. What is the value of \(\cos A\) in this triangle?
4. How do you determine the opposite side if it wasn't given?
5. How do you solve for angle \(C\) given \(\cos C\)?
6. What is the relationship between \(\cos C\) and \(\cos A\) in a right triangle?
7. How do you find \(\cos C\) if the hypotenuse and adjacent side are unknown?
8. What is the significance of the cosine function in trigonometry?

**Tip:** Remember, in a right triangle, the cosine of an angle represents the ratio of the length of the adjacent side to the length of the hypotenuse, which helps determine the relative size of the angle.

Learn how to calculate \( \cos C \) in a right triangle where the adjacent side \( AB \) measures 15 units and the hypotenuse \( AC \) measures 17 units. Understand the concept of cosine in trigonometry and its application in right triangles. Suitable for high school students studying trigonometry.

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