Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle VWU\), we know the side opposite to the angle \( \angle W = 68^{\circ}\) (side \(VU = 96\)) and we need to find the hypotenuse \(x\) (side \(WU\)). We use the sine ratio. The sine of an angle in a right - triangle is defined as \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \( \sin W=\frac{VU}{WU}\).

Step2: Substitute the values

Since \(W = 68^{\circ}\), \(VU = 96\), and \(WU=x\), we have \( \sin68^{\circ}=\frac{96}{x}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x=\frac{96}{\sin68^{\circ}}\). We know that \( \sin68^{\circ}\approx0.9272\). Then \(x=\frac{96}{0.9272}\approx103.5\).

Answer:

\(103.5\)