Question

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

Explanation:

Step1: Use trigonometric function

In right - triangle \(GHI\) with \(\angle G = 22^{\circ}\), \(\angle H=90^{\circ}\), and \(IH = 96\). We use the tangent function \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan G=\frac{IH}{GH}\), so \(x = GH\), and \(\tan22^{\circ}=\frac{96}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{96}{\tan22^{\circ}}\). Since \(\tan22^{\circ}\approx0.4040\), then \(x=\frac{96}{0.4040}\approx39.9\).

Answer:

\(x = 39.9\)