Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 38^{\circ}\), the hypotenuse \(= 1.5\), and the side opposite to the \(38^{\circ}\) angle is \(x\). So we use the sine ratio: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).

Step2: Substitute the values into the sine formula

Substitute \(\theta = 38^{\circ}\) and hypotenuse \(=1.5\) into \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). We get \(\sin(38^{\circ})=\frac{x}{1.5}\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(\sin(38^{\circ})=\frac{x}{1.5}\) by \(1.5\). Since \(\sin(38^{\circ})\approx0.6157\), then \(x = 1.5\times\sin(38^{\circ})\).
\(x=1.5\times0.6157 = 0.92355\)

Answer:

\(x\approx0.9\)