Question

question 5 of 10
the ____ of an angle is the ratio of the adjacent leg length to the hypotenuse
length.

a. cosine
b. tangent
c. sine

Explanation:

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

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

Given that the ratio is of the adjacent leg length to the hypotenuse length, this matches the definition of cosine.

Answer:

A. cosine