Question

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

Explanation:

Step1: Use the sine function definition

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 19^{\circ}\), the hypotenuse \(US = 9.9\), and the opposite side to \(\theta\) is \(x\) (side \(UT\)).
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 \(9.9\).
\(x = 9.9\times\sin(19^{\circ})\).
We know that \(\sin(19^{\circ})\approx0.3256\).
Then \(x = 9.9\times0.3256\).
\(x\approx3.2\).

Answer:

\(x\approx3.2\)