Question

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

answer

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(UST\), we know the hypotenuse \(US = 2.4\) and the side opposite to 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 \(x\)

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:

\(27.3\)