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, \(\theta = 69^{\circ}\), the opposite side to \(\theta\) is \(x\) (side \(NO\)), and the adjacent side is \(80\) (side \(OP\)). So, \(\tan(69^{\circ})=\frac{x}{80}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(69^{\circ})=\frac{x}{80}\) by \(80\). We know that \(\tan(69^{\circ})\approx2.605\). Then \(x = 80\times\tan(69^{\circ})\). Substitute the value of \(\tan(69^{\circ})\): \(x=80\times2.605\).

Answer:

\(x = 208.4\)