Question

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

Explanation:

Step1: Use the sine function

In a right - triangle, the sine of an angle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 19^{\circ}\), the hypotenuse \(SU = 9.9\), and the side opposite to \(\angle S\) is \(UT=x\). So, \(\sin(19^{\circ})=\frac{x}{9.9}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(19^{\circ})=\frac{x}{9.9}\) by \(9.9\). We get \(x = 9.9\times\sin(19^{\circ})\).
Since \(\sin(19^{\circ})\approx0.3256\), then \(x=9.9\times0.3256\).
\(x = 3.22344\approx3.2\)

Answer:

\(x\approx3.2\)