In a right triangle, which of the following ratios represents the cosine of angle $\theta$?

• A. $\frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}$
• B. $\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}$
• C. $\frac{\mathrm{opposite}}{\mathrm{adjacent}}$
• D.

Answer: (A)

Verified step by step guidance

1. Recall the definition of cosine in a right triangle: cosine of an angle \( \theta \) is the ratio of the length of the side adjacent to \( \theta \) to the length of the hypotenuse.
2. Identify the sides of the triangle relative to angle \( \theta \): the 'adjacent' side is the one next to \( \theta \) (but not the hypotenuse), the 'opposite' side is across from \( \theta \), and the 'hypotenuse' is the longest side opposite the right angle.
3. Write the cosine ratio as \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
4. Compare this ratio to the given options to determine which one matches the cosine definition.
5. Conclude that the ratio representing cosine of angle \( \theta \) is the one with 'adjacent' over 'hypotenuse'.