Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 72^{\circ}\), the adjacent side to \(\theta\) is \(YT = 3.9\), and the hypotenuse is \(YW=x\). So, \(\cos(72^{\circ})=\frac{3.9}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(\cos(72^{\circ})=\frac{3.9}{x}\) to get \(x=\frac{3.9}{\cos(72^{\circ})}\).
We know that \(\cos(72^{\circ})\approx0.3090\). Then \(x=\frac{3.9}{0.3090}\).

Step3: Calculate the value of \(x\)

\(x=\frac{3.9}{0.3090}\approx12.6\)

Answer:

\(x\approx12.6\)