The _____ of an angle is the ratio of the opposite leg length to the hypotenuse length.A.cosineB.sineC.tangent

Step 1: Break Down the Problem

The problem asks for the trigonometric function that represents the ratio of the length of the opposite side of a right-angled triangle to the length of the hypotenuse.

Step 2: Relevant Concepts

In trigonometry:

• The sine of an angle ($\theta$) is defined as: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

• The cosine of an angle ($\theta$) is defined as: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

• The tangent of an angle ($\theta$) is defined as: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step 3: Analysis and Detail

Based on the definitions:

• The sine function directly corresponds to the relationship described in the question. It indicates how the length of the opposite side compares to the hypotenuse.

Step 4: Verify and Summarize

Upon verifying the definitions, it's clear that the sine function is indeed the one that finds the ratio of the opposite leg to the hypotenuse.

Final Answer

The correct answer is B. sine.