Question

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

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse is \(20\), and the opposite side is \(z\). So, \(\sin30^{\circ}=\frac{z}{20}\).

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

Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{z}{20}\).

Step3: Solve for \(z\)

Cross - multiply: \(z=\frac{20\times1}{2}\).

Answer:

\(z = 10\)