Question

which equation would be used to solve for x? (see yellow hint below.) tan 18 = 29/x cos 18 = x/29 cos 18 = 29/x tan 18 = x/29

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the angle \(\theta = 18^{\circ}\), the adjacent side to the \(18^{\circ}\) angle is \(29\) cm, and the hypotenuse is \(x\).

Step2: Apply the cosine ratio

Using the formula \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), substituting \(\theta = 18^{\circ}\), adjacent \(= 29\), and hypotenuse \(=x\), we get \(\cos18=\frac{29}{x}\)

Answer:

\(\cos18=\frac{29}{x}\) (the third option)