Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 35^{\circ}\), the opposite side to the \(35^{\circ}\) angle is \(x\), and the hypotenuse is \(5\).

Step2: Set up the equation

Using the sine formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), we have \(\sin(35^{\circ})=\frac{x}{5}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(5\): \(x = 5\times\sin(35^{\circ})\).
We know that \(\sin(35^{\circ})\approx0.5736\). Then \(x = 5\times0.5736=2.868\).

Answer:

\(x\approx2.9\)