Question

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

Explanation:

Step1: Recall the sine function

In a right - triangle, the sine of an angle \(x\) is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(YT = 1.1\) and the hypotenuse \(US=2.4\). So, \(\sin x=\frac{1.1}{2.4}\).

Step2: Calculate the value of \(x\)

We know that \(x = \sin^{-1}(\frac{1.1}{2.4})\). First, calculate \(\frac{1.1}{2.4}\approx0.4583\). Then, \(x=\sin^{-1}(0.4583)\). Using a calculator, \(x\approx27.3^{\circ}\).

Answer:

\(27.3^{\circ}\)