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, \(\theta = 29^{\circ}\), the opposite side is \(x\), and the adjacent side is \(6.8\). So, \(\tan(29^{\circ})=\frac{x}{6.8}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(29^{\circ})=\frac{x}{6.8}\) by \(6.8\). We get \(x = 6.8\times\tan(29^{\circ})\).
We know that \(\tan(29^{\circ})\approx0.5543\). Then \(x=6.8\times0.5543\).
\(x = 6.8\times0.5543=3.76924\).

Answer:

\(x\approx3.8\)