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 \(VU\) (but we need to confirm the sides. Wait, no, for angle \(x\) in right - triangle \(VWU\) with right - angle at \(V\), \(\sin x=\frac{VU}{WU}\). Wait, no, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite to \(x\) is \(VU\) (wait no, in right - triangle \(VWU\) with \(\angle V = 90^{\circ}\), \(\sin x=\frac{VU}{WU}\) is wrong. Wait, \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\), the side opposite to \(x\) is \(VU\) (no, wait, \(\angle W=x\), side \(VU\) is opposite to \(\angle W\), and hypotenuse \(WU = 84\), adjacent side \(VW = 50\). So \(\sin x=\frac{VU}{WU}\) is wrong. Wait, \(\cos x=\frac{VW}{WU}\) (adjacent over hypotenuse).
\(\cos x=\frac{50}{84}\)

Step2: Calculate \(x\)

\(x=\cos^{- 1}(\frac{50}{84})\)
\(x=\cos^{-1}(\frac{25}{42})\approx53.8^{\circ}\)

Answer:

\(53.8^{\circ}\)