Question

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

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, we know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 34^{\circ}\), the opposite side is \(x\) and the adjacent side is \(19\). So, \(\tan(34^{\circ})=\frac{x}{19}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(34^{\circ})=\frac{x}{19}\) by \(19\). We get \(x = 19\times\tan(34^{\circ})\).
Since \(\tan(34^{\circ})\approx0.6745\), then \(x=19\times0.6745 = 12.8155\approx12.8\)

Answer:

\(12.8\)