Question

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

Explanation:

Step1: Use sine function

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

Step2: Calculate \(x\)

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

Answer:

\(27.3^{\circ}\)