Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle UTS\) with right - angle at \(T\), we know the hypotenuse \(US = 2.4\) and the opposite side to the angle \(x\) is \(UT=1.1\). 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, \(\sin x=\frac{1.1}{2.4}\).

Step2: Solve for \(x\)

We have \(\sin x=\frac{1.1}{2.4}\approx0.4583\). To find \(x\), we take the inverse sine (arcsin) of \(0.4583\). So, \(x = \sin^{- 1}(0.4583)\). Using a calculator, \(x\approx27.3^{\circ}\).

Answer:

\(x\approx27.3^{\circ}\)