Question

which equation describes the tangent function for a right triangle?
a. tan(θ)=opposite/adjacent
b. tan(θ)=adjacent/hypotenuse
c. tan(θ)=hypotenuse/opposite
d. tan(θ)=hypotenuse/adjacent

Explanation:

Step1: Recall trigonometric ratio definitions

In a right - triangle, for an acute angle \(\theta\), the trigonometric ratios are defined based on the sides (opposite, adjacent, hypotenuse).

Step2: Check each option

• Option A: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\) is the correct formula for the tangent function.
• Option B: \(\frac{\text{adjacent}}{\text{hypotenuse}}\) is the formula for the cosine function (\(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)), not tangent.
• Option C: \(\frac{\text{hypotenuse}}{\text{opposite}}\) is the reciprocal of the sine function (\(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\)), not tangent.
• Option D: \(\frac{\text{hypotenuse}}{\text{adjacent}}\) is the reciprocal of the cosine function (\(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)), not tangent.

Answer:

A. \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)