Which trig ratio is opposite over adjacent?

Which trig ratio is opposite over adjacent?

• A. SINE
• B. COSINE
• C. TANGENT
• D. COTANGENT

Answer: (C)

In a right triangle, the ratio formed by the side opposite the angle and the side adjacent to the angle is what tells you how steep the angle is. That ratio is defined as tangent. So when you see opposite over adjacent, that’s the tangent ratio. To see why the others don’t fit: sine uses opposite over the hypotenuse, which involves the longest side, not the adjacent. Cosine uses adjacent over the hypotenuse, again involving the hypotenuse. Cotangent is the reciprocal of tangent, which is adjacent over opposite, the inverse of what’s asked. So the only one that matches opposite over adjacent is tangent. For example, if opposite is 3 and adjacent is 4, tangent is 3/4, illustrating this exact relationship.

In a right triangle, the ratio formed by the side opposite the angle and the side adjacent to the angle is what tells you how steep the angle is. That ratio is defined as tangent. So when you see opposite over adjacent, that’s the tangent ratio.

To see why the others don’t fit: sine uses opposite over the hypotenuse, which involves the longest side, not the adjacent. Cosine uses adjacent over the hypotenuse, again involving the hypotenuse. Cotangent is the reciprocal of tangent, which is adjacent over opposite, the inverse of what’s asked. So the only one that matches opposite over adjacent is tangent. For example, if opposite is 3 and adjacent is 4, tangent is 3/4, illustrating this exact relationship.