Question

the ____ of an angle is the ratio of the opposite leg length to the hypotenuse length. a. sine b. cosine c. tangent

Explanation:

To solve this, we recall the definitions of trigonometric ratios in a right triangle:

• Sine of an angle ($\sin\theta$) is defined as the ratio of the length of the opposite leg to the length of the hypotenuse, i.e., $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
• Cosine of an angle ($\cos\theta$) is the ratio of the adjacent leg to the hypotenuse, i.e., $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.
• Tangent of an angle ($\tan\theta$) is the ratio of the opposite leg to the adjacent leg, i.e., $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Given the description in the question (ratio of opposite leg to hypotenuse), this matches the definition of sine.

Answer:

A. sine