Question

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

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 22^{\circ}\), the opposite side to \(\angle G\) is \(IH = 96\), and the adjacent side is \(GH=x\). So, \(\tan(22^{\circ})=\frac{IH}{GH}\).

Step2: Solve for \(x\)

Since \(\tan(22^{\circ})=\frac{96}{x}\), we can rewrite it as \(x=\frac{96}{\tan(22^{\circ})}\).
We know that \(\tan(22^{\circ})\approx0.4040\). Then \(x=\frac{96}{0.4040}\approx237.6\).

Answer:

\(x\approx237.6\)