Question

solve for $x$. round to the nearest tenth, if necessary.
answer attempt 1 out of 3
$x=$

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(UVW\), we know the hypotenuse \(UW = 4\) and we want to find the side \(VW=x\) opposite to the angle \(\angle U=28^{\circ}\). The sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin(28^{\circ})=\frac{x}{4}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(28^{\circ})=\frac{x}{4}\) by \(4\) to isolate \(x\).
We get \(x = 4\times\sin(28^{\circ})\).
Using a calculator, \(\sin(28^{\circ})\approx0.4695\).
Then \(x = 4\times0.4695=1.878\approx1.9\).

Answer:

\(1.9\)