Question

solve for x. round your answer to the nearest tenth.

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 54^{\circ}\), the opposite side to the angle \(\theta\) is \(x\), and the adjacent side is \(9\). So, \(\tan(54^{\circ})=\frac{x}{9}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(54^{\circ})=\frac{x}{9}\) by \(9\). We get \(x = 9\times\tan(54^{\circ})\).
Since \(\tan(54^{\circ})\approx1.376\), then \(x=9\times1.376 = 12.384\).

Answer:

\(12.4\)