Question

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

Explanation:

Step1: Recall trigonometric - ratio definitions

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

Step2: Select the correct trigonometric ratio

Since $\tan24^{\circ}=\frac{\text{opposite}}{\text{adjacent}}=\frac{x}{12}$.

Answer:

$\tan24 = x/12$