Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(YTW\) with \(\angle W = 31^{\circ}\), hypotenuse \(YW=95\), and side \(YT = x\). We use the sine function since \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 31^{\circ}\), opposite side to \(\angle W\) is \(YT\) and hypotenuse is \(YW\).
So, \(\sin(31^{\circ})=\frac{x}{95}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(31^{\circ})=\frac{x}{95}\) by \(95\).
\(x = 95\times\sin(31^{\circ})\).
We know that \(\sin(31^{\circ})\approx0.515\).
Then \(x=95\times0.515 = 48.925\).

Answer:

\(x\approx48.9\)