Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(GH = 3\) and the hypotenuse is \(FH=4.2\). So, \(\sin x=\frac{3}{4.2}\).

Step2: Solve for \(x\)

We know that \(x = \sin^{-1}(\frac{3}{4.2})\). First, calculate \(\frac{3}{4.2}=\frac{30}{42}=\frac{5}{7}\approx0.714\). Then, \(x=\sin^{-1}(0.714)\). Using a calculator, \(x\approx45.6^{\circ}\).

Answer:

\(45.6^{\circ}\)