Question

write the correct equation for this problem. do not solve.

Explanation:

Step1: Identify triangle type

It's a right - triangle with one angle \(58^{\circ}\), hypotenuse \(11\), and adjacent side to \(58^{\circ}\) is \(x\).

Step2: Recall trigonometric ratio

For cosine, \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 58^{\circ}\), adjacent \(=x\), hypotenuse \( = 11\). So the equation is \(\cos(58^{\circ})=\frac{x}{11}\) or \(x = 11\times\cos(58^{\circ})\) (either form is correct for the equation).

Answer:

\(\cos(58^{\circ})=\frac{x}{11}\) (or \(x = 11\cos(58^{\circ})\))