Question

solve for x. round to the nearest tenth, if necessary.
3.2
38°
x

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 38^{\circ}\), the hypotenuse \(= 3.2\), and the side opposite to \(\theta\) is \(x\).

Step2: Set up the equation

Using the sine formula \(\sin(38^{\circ})=\frac{x}{3.2}\).

Step3: Solve for \(x\)

Multiply both sides by \(3.2\): \(x = 3.2\times\sin(38^{\circ})\).
We know that \(\sin(38^{\circ})\approx0.6157\).
So \(x = 3.2\times0.6157=1.97024\).

Answer:

\(x\approx2.0\)