Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle UTS\) with right - angle at \(T\), we know the opposite side (\(UT = 1.1\)) and the hypotenuse (\(US=2.4\)). We use the sine ratio. The sine of an angle \(x\) in a right - triangle is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin x=\frac{1.1}{2.4}\).

Step2: Solve for \(x\)

Take the inverse - sine (arcsin) of both sides. \(x = \sin^{-1}(\frac{1.1}{2.4})\).
Calculate \(\frac{1.1}{2.4}\approx0.4583\). Then \(x=\sin^{-1}(0.4583)\). Using a calculator, \(x\approx27.3^{\circ}\).

Answer:

\(27.3\)