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 side opposite to angle \(x\) is \(TS = 5\) and the hypotenuse is \(US=7.2\). So, \(\sin x=\frac{5}{7.2}\).

Step2: Calculate \(x\)

\(x = \sin^{-1}(\frac{5}{7.2})\). First, \(\frac{5}{7.2}\approx0.6944\). Then, \(x=\sin^{-1}(0.6944)\). Using a calculator, \(x\approx44.0^{\circ}\).

Answer:

\(44.0\)