Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(WTY\), \(\sin W=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(W = 48^{\circ}\), the hypotenuse \(WY = 52\), and the side opposite to angle \(W\) is \(x\).

Step2: Set up the equation

We know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin48^{\circ}=\frac{x}{52}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(52\): \(x = 52\times\sin48^{\circ}\).
Since \(\sin48^{\circ}\approx0.7431\), then \(x = 52\times0.7431\).
\(x=38.6412\approx38.6\)

Answer:

\(x = 38.6\)