Question

solve for z. do not convert your answer to decimal form. rationalize the denominato and simplify your answer if necessary.

Explanation:

Step1: Use the sine function

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

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

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

Step3: Solve for \(z\)

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

Answer:

\(z = 16\)