Question

cos 24 = x / 12
tan 24 = x / 12
sin 24 = x / 12
which is the correct set up to solve for x?

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For an angle of $24^{\circ}$ in the given right - triangle, the side opposite the $24^{\circ}$ angle is $x$ and the side adjacent to the $24^{\circ}$ angle is $12$.

Step2: Determine the correct trigonometric ratio

Since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, when $\theta = 24^{\circ}$, $\text{opposite}=x$ and $\text{adjacent}=12$, we have $\tan24^{\circ}=\frac{x}{12}$.

Answer:

$\tan24 = x/12$