Given a right triangle with vertices labeled x, z, and w, and angle $xzw$, what is the cosine ratio of angle $xzw$?

• A. The ratio of the length of the side adjacent to angle $xzw$ to the length of the hypotenuse
• B. The ratio of the length of the side adjacent to angle $xzw$ to the length of the side opposite angle $xzw$
• C. The ratio of the length of the hypotenuse to the length of the side adjacent to angle $xzw$
• D. The ratio of the length of the side opposite angle $xzw$ to the length of the hypotenuse

Answer: (A)

Verified step by step guidance

1. Identify the angle in question, which is angle \( xzw \), located at vertex \( z \) of the right triangle.
2. Recall the definition of the cosine of an angle in a right triangle: \( \cos(\theta) = \frac{\text{length of adjacent side}}{\text{length of hypotenuse}} \).
3. Determine which side is adjacent to angle \( xzw \). This is the side that forms the angle \( xzw \) along with the hypotenuse, excluding the side opposite the angle.
4. Identify the hypotenuse, which is the longest side of the right triangle and is opposite the right angle.
5. Write the cosine ratio for angle \( xzw \) as the ratio of the length of the side adjacent to angle \( xzw \) to the length of the hypotenuse: \( \cos(xzw) = \frac{\text{adjacent side}}{\text{hypotenuse}} \).