Question

for x. do not convert your answer to decimal form. rationalize th
mplify your answer if necessary.
draw
30°
8

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the opposite side to the \(30^{\circ}\) angle is \(8\), and the hypotenuse is \(x\).
So, \(\sin30^{\circ}=\frac{8}{x}\).

Step2: Substitute the value of \(\sin30^{\circ}\)

Since \(\sin30^{\circ}=\frac{1}{2}\), we have the equation \(\frac{1}{2}=\frac{8}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(x\times1 = 8\times2\).

Answer:

\(x = 16\)