Question

a calculator is allowed for this question.
solve for x. (round to the nearest thousandth.) show all work.
select the \insert\ drop - down option in the menu below and use \√x equation\ to type your answer when you need to incorporate symbols, equations, or other math expressions.

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, the hypotenuse is 8, and \( x \) is the side adjacent to the \( 72^\circ \) angle. The cosine function relates the adjacent side and the hypotenuse: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(72^\circ)=\frac{x}{8} \).

Step2: Solve for \( x \)

Multiply both sides by 8: \( x = 8\times\cos(72^\circ) \). Calculate \( \cos(72^\circ) \approx 0.3090 \), then \( x = 8\times0.3090 = 2.472 \).

Answer:

\( 2.472 \)