Question

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

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 72^{\circ}\), the opposite side to \(\theta\) is \(x\) and the adjacent side is \(13\). So, \(\tan(72^{\circ})=\frac{x}{13}\).

Step2: Solve for \(x\)

We know that \(\tan(72^{\circ})\approx3.0777\). Then \(x = 13\times\tan(72^{\circ})\). Substitute the value of \(\tan(72^{\circ})\): \(x=13\times3.0777 = 39.9901\approx40.0\)

Answer:

\(40.0\)