Question

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

Explanation:

Step1: Use trigonometric ratio

In right - triangle \( \triangle FGE\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 71^{\circ}\), the opposite side to \(\angle G\) is \(FE=x\) and the adjacent side is \(FG = 8.1\). So, \(\tan(71^{\circ})=\frac{x}{8.1}\).

Step2: Solve for \(x\)

We know that \(\tan(71^{\circ})\approx2.9042\). Then \(x = 8.1\times\tan(71^{\circ})\). Substitute \(\tan(71^{\circ})\approx2.9042\) into the equation: \(x=8.1\times2.9042\).

$$x = 23.52402\approx23.5$$

Answer:

\(23.5\)