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, \(\theta = 56^{\circ}\), the opposite side to \(\theta\) is \(x\), and the hypotenuse is \(86\). So, \(\sin(56^{\circ})=\frac{x}{86}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(56^{\circ})=\frac{x}{86}\) by \(86\). We know that \(\sin(56^{\circ})\approx0.829\). Then \(x = 86\times\sin(56^{\circ})\).

$$x=86\times0.829 = 71.3$$

Answer:

\(71.3\)