Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, we use the sine function. The formula for sine is \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is not needed. We can also use the cosine function. But more straightforwardly, using the definition of \(\sin\) in the context of right - triangle (if we consider the right - triangle \( \triangle PQO\) with right - angle at \(P\)), \(\sin(x)=\frac{PO}{QO}\) (incorrect approach). A better approach is using the cosine function: \(\cos(x)=\frac{PQ}{QO}\) (where \(PQ = 73\) and \(QO=97\)).

Step2: Calculate the angle

We know that \(x=\cos^{- 1}(\frac{73}{97})\). First, calculate \(\frac{73}{97}\approx0.7526\). Then, \(x = \cos^{-1}(0.7526)\). Using a calculator, \(x\approx41.1^{\circ}\)

Answer:

\(x\approx41.1^{\circ}\)