Question

4/10
which is the correct set up to solve for x?
tan 24 = x / 12
cos 24 = x / 12
sin 24 = x / 12

Explanation:

Step1: Recall trigonometric ratios

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

Step2: Apply the tangent ratio

Since \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), substituting \(\theta = 24^{\circ}\), opposite \(=x\) and adjacent \( = 12\), we get \(\tan24^{\circ}=\frac{x}{12}\).

Answer:

\(\tan24 = x/12\)