Question

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

Explanation:

Step1: Use the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 29^{\circ}\), the opposite side is \(x\) and the hypotenuse is \(6.8\). So, \(\sin(29^{\circ})=\frac{x}{6.8}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(29^{\circ})=\frac{x}{6.8}\) by \(6.8\). We get \(x = 6.8\times\sin(29^{\circ})\).
Since \(\sin(29^{\circ})\approx0.485\), then \(x=6.8\times0.485 = 3.3\).

Answer:

\(x = 3.3\)