trigonometric ratio definition

Check the final answer first, then review the worked steps.

Problem

trigonometric ratio definition

Answer

B. sine

Step-by-step solution

1. Identify the trigonometric definitions: In a right-angled triangle, the three primary trigonometric ratios for an angle $\theta$ are defined as follows:
- The sine of an angle is the ratio of the length of the opposite leg to the length of the hypotenuse: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.
- The cosine of an angle is the ratio of the length of the adjacent leg to the length of the hypotenuse: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.
- The tangent of an angle is the ratio of the length of the opposite leg to the length of the adjacent leg: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

  1. Match the definition to the question: The question asks for the ratio of the 'opposite leg length' to the 'hypotenuse length'. Based on the definitions above, this corresponds to the sine function.
  1. Conclusion: Therefore, the correct term is 'sine', which corresponds to option B.