Question

which equation is correct?
○ cos x° = adjacent ÷ hypotenuse
○ tan x° = hypotenuse ÷ adjacent
○ cos x° = hypotenuse ÷ adjacent
○ tan x° = adjacent ÷ hypotenuse

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, the cosine of an angle \(x^{\circ}\) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Mathematically, \(\cos x^{\circ}=\frac{\text{adjacent}}{\text{hypotenuse}}\) (which is the same as adjacent \(\div\) hypotenuse).

The tangent of an angle \(x^{\circ}\) is defined as the ratio of the length of the opposite side to the length of the adjacent side, i.e., \(\tan x^{\circ}=\frac{\text{opposite}}{\text{adjacent}}\) (opposite \(\div\) adjacent).

Let's analyze each option:

• Option 1: \(\cos x^{\circ}=\text{adjacent}\div\text{hypotenuse}\) - This matches the definition of cosine.
• Option 2: \(\tan x^{\circ}=\text{hypotenuse}\div\text{adjacent}\) - This is incorrect. The correct formula for tangent is \(\tan x^{\circ}=\text{opposite}\div\text{adjacent}\).
• Option 3: \(\cos x^{\circ}=\text{hypotenuse}\div\text{adjacent}\) - This is incorrect. The correct formula for cosine is \(\cos x^{\circ}=\text{adjacent}\div\text{hypotenuse}\).
• Option 4: \(\tan x^{\circ}=\text{adjacent}\div\text{hypotenuse}\) - This is incorrect. The correct formula for tangent is \(\tan x^{\circ}=\text{opposite}\div\text{adjacent}\), and the formula \(\text{adjacent}\div\text{hypotenuse}\) is for cosine (not tangent).

Answer:

\(\boldsymbol{\cos x^{\circ}=\text{adjacent}\div\text{hypotenuse}}\) (the first option)