Question

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

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 31^{\circ}\), the hypotenuse \(yN = 95\), and the side opposite to \(\theta\) is \(x\) (i.e., \(yT\)). So, \(\sin(31^{\circ})=\frac{x}{95}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(31^{\circ})=\frac{x}{95}\) by \(95\). We get \(x = 95\times\sin(31^{\circ})\).
Since \(\sin(31^{\circ})\approx0.515\), then \(x=95\times0.515 = 48.925\approx48.9\).

Answer:

\(48.9\)