Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 28^{\circ}\), the hypotenuse \(LJ = 95\), and the side opposite to \(\theta\) is \(JK=x\).

Step2: Set up the equation

Using the sine formula \(\sin(28^{\circ})=\frac{x}{95}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(95\): \(x = 95\times\sin(28^{\circ})\).
We know that \(\sin(28^{\circ})\approx0.4695\).
So, \(x=95\times0.4695 = 44.6025\approx44.6\)

Answer:

\(44.6\)