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 \(WV = 7.5\) and the hypotenuse is \(WU=9.5\). So, \(\sin x=\frac{7.5}{9.5}\).

Step2: Solve for \(x\)

Take the inverse sine (arcsin) of both sides. \(x = \sin^{-1}(\frac{7.5}{9.5})\).
Calculate \(\frac{7.5}{9.5}\approx0.7895\).
Then \(x=\sin^{-1}(0.7895)\).
Using a calculator, \(x\approx52.2^{\circ}\).

Answer:

\(x\approx52.2^{\circ}\)