In a right triangle, what is the tangent ratio for angle $\theta$?

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

Answer: (A)

Verified step by step guidance

1. Recall that in a right triangle, the tangent of an angle \( \theta \) is defined as the ratio of the length of the side opposite to \( \theta \) to the length of the side adjacent to \( \theta \).
2. Identify the sides relative to the angle \( \theta \): the 'opposite' side is the one directly across from \( \theta \), the 'adjacent' side is the one next to \( \theta \) (but not the hypotenuse), and the 'hypotenuse' is the longest side opposite the right angle.
3. Write the tangent ratio formula as: \[\text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]
4. Understand that the other given ratios, such as \( \frac{\text{hypotenuse}}{\text{opposite}} \) or \( \frac{\text{adjacent}}{\text{hypotenuse}} \), correspond to other trigonometric functions (like cosecant or cosine), not tangent.
5. Therefore, to find the tangent ratio for angle \( \theta \), always use the ratio of the opposite side over the adjacent side.