In a right triangle, which ratio defines tangent?

In a right triangle, which ratio defines tangent?

• A. Opposite/Hypotenuse
• B. Adjacent/Hypotenuse
• C. Opposite/Adjacent
• D. Hypotenuse/Adjacent

Answer: (C)

Tangent is defined for a chosen acute angle in a right triangle as the ratio of the length of the side opposite that angle to the length of the side adjacent to that angle. The side opposite is the one across from the angle, and the side adjacent is the leg that forms the angle with the other leg (not the hypotenuse). The hypotenuse is the longest side opposite the right angle. So, tan(angle) = opposite / adjacent. That’s why the ratio of opposite to adjacent is the tangent, and why the other ratios involve the hypotenuse (sine and cosine use opposite/hypotenuse and adjacent/hypotenuse, respectively) or the secant (hypotenuse/adjacent).

Tangent is defined for a chosen acute angle in a right triangle as the ratio of the length of the side opposite that angle to the length of the side adjacent to that angle. The side opposite is the one across from the angle, and the side adjacent is the leg that forms the angle with the other leg (not the hypotenuse). The hypotenuse is the longest side opposite the right angle. So, tan(angle) = opposite / adjacent. That’s why the ratio of opposite to adjacent is the tangent, and why the other ratios involve the hypotenuse (sine and cosine use opposite/hypotenuse and adjacent/hypotenuse, respectively) or the secant (hypotenuse/adjacent).