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 is \(x\) and the adjacent side is \(96\). So, \(\tan(22^{\circ})=\frac{x}{96}\).

Step2: Solve for \(x\)

We know that \(\tan(22^{\circ})\approx0.404\). Then \(x = 96\times\tan(22^{\circ})\). Substituting the value of \(\tan(22^{\circ})\), we get \(x=96\times0.404 = 37.2\).

Answer:

\(x = 37.2\)